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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 17424cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.g2 | 17424cd1 | \([0, 0, 0, -570999, 189073874]\) | \(-4253392/729\) | \(-3528757982049290496\) | \([]\) | \(354816\) | \(2.2853\) | \(\Gamma_0(N)\)-optimal |
| 17424.g1 | 17424cd2 | \([0, 0, 0, -48007839, 128031357674]\) | \(-2527934627152/9\) | \(-43564913358633216\) | \([]\) | \(1064448\) | \(2.8346\) |
Rank
sage: E.rank()
The elliptic curves in class 17424cd have rank \(0\).
Complex multiplication
The elliptic curves in class 17424cd do not have complex multiplication.Modular form 17424.2.a.cd
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.
