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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 141120gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.ne2 | 141120gh1 | \([0, 0, 0, -193452, -31462704]\) | \(2803221/125\) | \(35702288842752000\) | \([2]\) | \(1376256\) | \(1.9388\) | \(\Gamma_0(N)\)-optimal |
| 141120.ne1 | 141120gh2 | \([0, 0, 0, -522732, 104068944]\) | \(55306341/15625\) | \(4462786105344000000\) | \([2]\) | \(2752512\) | \(2.2854\) |
Rank
sage: E.rank()
The elliptic curves in class 141120gh have rank \(0\).
Complex multiplication
The elliptic curves in class 141120gh do not have complex multiplication.Modular form 141120.2.a.gh
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.
