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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 30576.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30576.l1 | 30576br4 | \([0, -1, 0, -16259784, 25241403888]\) | \(986551739719628473/111045168\) | \(53511589765251072\) | \([2]\) | \(1105920\) | \(2.6342\) | |
| 30576.l2 | 30576br3 | \([0, -1, 0, -1834184, -323669520]\) | \(1416134368422073/725251155408\) | \(349491499755912364032\) | \([2]\) | \(1105920\) | \(2.6342\) | |
| 30576.l3 | 30576br2 | \([0, -1, 0, -1018824, 392542704]\) | \(242702053576633/2554695936\) | \(1231083201226604544\) | \([2, 2]\) | \(552960\) | \(2.2876\) | |
| 30576.l4 | 30576br1 | \([0, -1, 0, -15304, 15219184]\) | \(-822656953/207028224\) | \(-99764893799940096\) | \([2]\) | \(276480\) | \(1.9410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30576.l have rank \(1\).
Complex multiplication
The elliptic curves in class 30576.l do not have complex multiplication.Modular form 30576.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
