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SageMath

sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 3850.m

sage: E.isogeny_class().curves

LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|

3850.m1 | 3850p2 | \([1, 0, 0, -1838, -30458]\) | \(43949604889/42350\) | \(661718750\) | \([2]\) | \(3072\) | \(0.61370\) | |

3850.m2 | 3850p1 | \([1, 0, 0, -88, -708]\) | \(-4826809/10780\) | \(-168437500\) | \([2]\) | \(1536\) | \(0.26713\) | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 3850.m have rank \(0\).

## Complex multiplication

The elliptic curves in class 3850.m do not have complex multiplication.## Modular form 3850.2.a.m

sage: E.q_eigenform(10)

## Isogeny matrix

sage: E.isogeny_class().matrix()

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.