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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 393008h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393008.h1 | 393008h1 | \([0, 1, 0, -887, -3500]\) | \(2725888/1421\) | \(40278210896\) | \([2]\) | \(322560\) | \(0.72678\) | \(\Gamma_0(N)\)-optimal |
| 393008.h2 | 393008h2 | \([0, 1, 0, 3348, -23828]\) | \(9148592/5887\) | \(-2669869979392\) | \([2]\) | \(645120\) | \(1.0733\) |
Rank
sage: E.rank()
The elliptic curves in class 393008h have rank \(1\).
Complex multiplication
The elliptic curves in class 393008h do not have complex multiplication.Modular form 393008.2.a.h
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.
