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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 7935.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7935.j1 | 7935j3 | \([1, 0, 1, -15940633, -24488418157]\) | \(3026030815665395929/1364501953125\) | \(201995259673095703125\) | \([2]\) | \(633600\) | \(2.8540\) | |
7935.j2 | 7935j4 | \([1, 0, 1, -8762103, 9808700131]\) | \(502552788401502649/10024505152875\) | \(1483986532090931530875\) | \([4]\) | \(633600\) | \(2.8540\) | |
7935.j3 | 7935j2 | \([1, 0, 1, -1157728, -250367119]\) | \(1159246431432649/488076890625\) | \(72252896404027640625\) | \([2, 2]\) | \(316800\) | \(2.5074\) | |
7935.j4 | 7935j1 | \([1, 0, 1, 241477, -28733047]\) | \(10519294081031/8500170375\) | \(-1258330278114588375\) | \([2]\) | \(158400\) | \(2.1609\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7935.j have rank \(0\).
Complex multiplication
The elliptic curves in class 7935.j do not have complex multiplication.Modular form 7935.2.a.j
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.