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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 30345.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30345.z1 | 30345s4 | \([1, 0, 1, -85984, 9474407]\) | \(2912566550041/76531875\) | \(1847293413511875\) | \([2]\) | \(147456\) | \(1.7108\) | |
| 30345.z2 | 30345s2 | \([1, 0, 1, -12289, -312289]\) | \(8502154921/3186225\) | \(76907725787025\) | \([2, 2]\) | \(73728\) | \(1.3642\) | |
| 30345.z3 | 30345s1 | \([1, 0, 1, -10844, -435403]\) | \(5841725401/1785\) | \(43085560665\) | \([2]\) | \(36864\) | \(1.0176\) | \(\Gamma_0(N)\)-optimal |
| 30345.z4 | 30345s3 | \([1, 0, 1, 38286, -2213909]\) | \(257138126279/236782035\) | \(-5715342707772915\) | \([2]\) | \(147456\) | \(1.7108\) |
Rank
sage: E.rank()
The elliptic curves in class 30345.z have rank \(0\).
Complex multiplication
The elliptic curves in class 30345.z do not have complex multiplication.Modular form 30345.2.a.z
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.
