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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4851.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4851.c1 | 4851s2 | \([1, -1, 1, -1570190, 468188606]\) | \(14553591673375/5208653241\) | \(153227012551324319223\) | \([2]\) | \(143360\) | \(2.5741\) | |
4851.c2 | 4851s1 | \([1, -1, 1, 297445, 51332474]\) | \(98931640625/96059601\) | \(-2825860161364158303\) | \([2]\) | \(71680\) | \(2.2275\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4851.c have rank \(0\).
Complex multiplication
The elliptic curves in class 4851.c do not have complex multiplication.Modular form 4851.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.