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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 46410.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.bz1 | 46410ca4 | \([1, 0, 0, -73171, 7584245]\) | \(43325247696520145329/183535468285260\) | \(183535468285260\) | \([2]\) | \(270336\) | \(1.5912\) | |
| 46410.bz2 | 46410ca2 | \([1, 0, 0, -6871, -13735]\) | \(35874636409222129/20685941312400\) | \(20685941312400\) | \([2, 2]\) | \(135168\) | \(1.2446\) | |
| 46410.bz3 | 46410ca1 | \([1, 0, 0, -4871, -130935]\) | \(12781554414694129/36385440000\) | \(36385440000\) | \([2]\) | \(67584\) | \(0.89802\) | \(\Gamma_0(N)\)-optimal |
| 46410.bz4 | 46410ca3 | \([1, 0, 0, 27429, -102915]\) | \(2282194455855813071/1325495413520460\) | \(-1325495413520460\) | \([2]\) | \(270336\) | \(1.5912\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 46410.bz do not have complex multiplication.Modular form 46410.2.a.bz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
