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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 394944ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 394944.ev1 | 394944ev1 | \([0, 1, 0, -1517985, -719912481]\) | \(832972004929/610368\) | \(283457393642176512\) | \([2]\) | \(8847360\) | \(2.2830\) | \(\Gamma_0(N)\)-optimal |
| 394944.ev2 | 394944ev2 | \([0, 1, 0, -1208225, -1021928481]\) | \(-420021471169/727634952\) | \(-337916645395679674368\) | \([2]\) | \(17694720\) | \(2.6296\) |
Rank
sage: E.rank()
The elliptic curves in class 394944ev have rank \(1\).
Complex multiplication
The elliptic curves in class 394944ev do not have complex multiplication.Modular form 394944.2.a.ev
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 Cremona 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 Cremona labels.
