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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 206400gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.ft3 | 206400gh1 | \([0, 1, 0, -109633, -13991137]\) | \(35578826569/51600\) | \(211353600000000\) | \([2]\) | \(884736\) | \(1.6508\) | \(\Gamma_0(N)\)-optimal |
| 206400.ft2 | 206400gh2 | \([0, 1, 0, -141633, -5191137]\) | \(76711450249/41602500\) | \(170403840000000000\) | \([2, 2]\) | \(1769472\) | \(1.9974\) | |
| 206400.ft1 | 206400gh3 | \([0, 1, 0, -1341633, 593608863]\) | \(65202655558249/512820150\) | \(2100511334400000000\) | \([2]\) | \(3538944\) | \(2.3439\) | |
| 206400.ft4 | 206400gh4 | \([0, 1, 0, 546367, -40279137]\) | \(4403686064471/2721093750\) | \(-11145600000000000000\) | \([2]\) | \(3538944\) | \(2.3439\) |
Rank
sage: E.rank()
The elliptic curves in class 206400gh have rank \(0\).
Complex multiplication
The elliptic curves in class 206400gh do not have complex multiplication.Modular form 206400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
