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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 9016h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9016.m2 | 9016h1 | \([0, -1, 0, 205392, -5357092]\) | \(7953970437500/4703287687\) | \(-566617183321971712\) | \([2]\) | \(92160\) | \(2.0959\) | \(\Gamma_0(N)\)-optimal |
| 9016.m1 | 9016h2 | \([0, -1, 0, -831448, -42268596]\) | \(263822189935250/149429406721\) | \(36004291115661166592\) | \([2]\) | \(184320\) | \(2.4425\) |
Rank
sage: E.rank()
The elliptic curves in class 9016h have rank \(1\).
Complex multiplication
The elliptic curves in class 9016h do not have complex multiplication.Modular form 9016.2.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.
