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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 41650h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41650.z2 | 41650h1 | \([1, 0, 1, 1374, -51852]\) | \(375078431/1740800\) | \(-1332800000000\) | \([]\) | \(55296\) | \(1.0089\) | \(\Gamma_0(N)\)-optimal |
| 41650.z1 | 41650h2 | \([1, 0, 1, -12626, 1572148]\) | \(-290707016929/1228250000\) | \(-940378906250000\) | \([]\) | \(165888\) | \(1.5582\) |
Rank
sage: E.rank()
The elliptic curves in class 41650h have rank \(0\).
Complex multiplication
The elliptic curves in class 41650h do not have complex multiplication.Modular form 41650.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
