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SageMath
E = EllipticCurve("hz1")
E.isogeny_class()
Elliptic curves in class 388080hz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.hz1 | 388080hz1 | \([0, 0, 0, -35244867, 80532804674]\) | \(13782741913468081/701662500\) | \(246492655108761600000\) | \([2]\) | \(26542080\) | \(2.9828\) | \(\Gamma_0(N)\)-optimal |
| 388080.hz2 | 388080hz2 | \([0, 0, 0, -33339747, 89625180386]\) | \(-11666347147400401/3126621093750\) | \(-1098375835843440000000000\) | \([2]\) | \(53084160\) | \(3.3294\) |
Rank
sage: E.rank()
The elliptic curves in class 388080hz have rank \(1\).
Complex multiplication
The elliptic curves in class 388080hz do not have complex multiplication.Modular form 388080.2.a.hz
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.
