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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 7497.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7497.l1 | 7497o3 | \([1, -1, 0, -39993, -3068416]\) | \(82483294977/17\) | \(1458024057\) | \([2]\) | \(9216\) | \(1.1456\) | |
7497.l2 | 7497o2 | \([1, -1, 0, -2508, -47125]\) | \(20346417/289\) | \(24786408969\) | \([2, 2]\) | \(4608\) | \(0.79905\) | |
7497.l3 | 7497o4 | \([1, -1, 0, -303, -128710]\) | \(-35937/83521\) | \(-7163272192041\) | \([2]\) | \(9216\) | \(1.1456\) | |
7497.l4 | 7497o1 | \([1, -1, 0, -303, 944]\) | \(35937/17\) | \(1458024057\) | \([2]\) | \(2304\) | \(0.45248\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7497.l have rank \(0\).
Complex multiplication
The elliptic curves in class 7497.l do not have complex multiplication.Modular form 7497.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.