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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 55233.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55233.h1 | 55233p2 | \([0, 0, 1, -192774, -32595683]\) | \(-23100424192/14739\) | \(-505495336003011\) | \([]\) | \(344736\) | \(1.7623\) | |
| 55233.h2 | 55233p1 | \([0, 0, 1, 2166, -186908]\) | \(32768/459\) | \(-15742069287291\) | \([]\) | \(114912\) | \(1.2130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55233.h have rank \(0\).
Complex multiplication
The elliptic curves in class 55233.h do not have complex multiplication.Modular form 55233.2.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 LMFDB 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 LMFDB labels.
