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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 19404h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.bd2 | 19404h1 | \([0, 0, 0, 31752, 4491585]\) | \(95551488/290521\) | \(-10764083191265712\) | \([2]\) | \(138240\) | \(1.7596\) | \(\Gamma_0(N)\)-optimal |
| 19404.bd1 | 19404h2 | \([0, 0, 0, -292383, 52139430]\) | \(4662947952/717409\) | \(425291123638579968\) | \([2]\) | \(276480\) | \(2.1061\) |
Rank
sage: E.rank()
The elliptic curves in class 19404h have rank \(0\).
Complex multiplication
The elliptic curves in class 19404h do not have complex multiplication.Modular form 19404.2.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.
