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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 30030.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30030.c1 | 30030b4 | \([1, 1, 0, -2614278, -1626991848]\) | \(1975965129869527614498409/1480785368327204940\) | \(1480785368327204940\) | \([2]\) | \(884736\) | \(2.4197\) | |
| 30030.c2 | 30030b3 | \([1, 1, 0, -1652878, 807576112]\) | \(499397679770019630680809/6781140655749319860\) | \(6781140655749319860\) | \([2]\) | \(884736\) | \(2.4197\) | |
| 30030.c3 | 30030b2 | \([1, 1, 0, -197578, -14086268]\) | \(852987960666806845609/408907582475792400\) | \(408907582475792400\) | \([2, 2]\) | \(442368\) | \(2.0732\) | |
| 30030.c4 | 30030b1 | \([1, 1, 0, 44422, -1647468]\) | \(9693994288141282391/6808957515360000\) | \(-6808957515360000\) | \([2]\) | \(221184\) | \(1.7266\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30030.c have rank \(1\).
Complex multiplication
The elliptic curves in class 30030.c do not have complex multiplication.Modular form 30030.2.a.c
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.
