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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 323400h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.h1 | 323400h1 | \([0, -1, 0, -13390883, 18865336512]\) | \(9028656748079104/3969405\) | \(116749132211250000\) | \([2]\) | \(13271040\) | \(2.6163\) | \(\Gamma_0(N)\)-optimal |
| 323400.h2 | 323400h2 | \([0, -1, 0, -13323508, 19064497012]\) | \(-555816294307024/11837848275\) | \(-5570844046821900000000\) | \([2]\) | \(26542080\) | \(2.9629\) |
Rank
sage: E.rank()
The elliptic curves in class 323400h have rank \(2\).
Complex multiplication
The elliptic curves in class 323400h do not have complex multiplication.Modular form 323400.2.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.
