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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 70785e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70785.q1 | 70785e1 | \([0, 0, 1, -5082, -140088]\) | \(-303464448/1625\) | \(-77727238875\) | \([]\) | \(64800\) | \(0.93423\) | \(\Gamma_0(N)\)-optimal |
| 70785.q2 | 70785e2 | \([0, 0, 1, 13068, -745693]\) | \(7077888/10985\) | \(-383042942265555\) | \([]\) | \(194400\) | \(1.4835\) |
Rank
sage: E.rank()
The elliptic curves in class 70785e have rank \(1\).
Complex multiplication
The elliptic curves in class 70785e do not have complex multiplication.Modular form 70785.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
