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SageMath
E = EllipticCurve("ha1")
E.isogeny_class()
Elliptic curves in class 346560.ha
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.ha1 | 346560ha2 | \([0, 1, 0, -15537921, 14097213279]\) | \(4904335099/1822500\) | \(154166448410388725760000\) | \([2]\) | \(28016640\) | \(3.1493\) | |
| 346560.ha2 | 346560ha1 | \([0, 1, 0, -6758401, -6606650785]\) | \(403583419/10800\) | \(913578953543044300800\) | \([2]\) | \(14008320\) | \(2.8027\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.ha have rank \(0\).
Complex multiplication
The elliptic curves in class 346560.ha do not have complex multiplication.Modular form 346560.2.a.ha
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.
