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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 338800.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338800.eh1 | 338800eh1 | \([0, 0, 0, -18860875, -31519743750]\) | \(52355598021/15092\) | \(213891188896000000000\) | \([2]\) | \(16588800\) | \(2.8810\) | \(\Gamma_0(N)\)-optimal |
| 338800.eh2 | 338800eh2 | \([0, 0, 0, -16440875, -39905043750]\) | \(-34677868581/28471058\) | \(-403505727852304000000000\) | \([2]\) | \(33177600\) | \(3.2276\) |
Rank
sage: E.rank()
The elliptic curves in class 338800.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 338800.eh do not have complex multiplication.Modular form 338800.2.a.eh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
