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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 23520l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23520.n3 | 23520l1 | \([0, -1, 0, -11090, 444312]\) | \(20034997696/455625\) | \(3430644840000\) | \([2, 2]\) | \(55296\) | \(1.1920\) | \(\Gamma_0(N)\)-optimal |
23520.n4 | 23520l2 | \([0, -1, 0, 1160, 1360612]\) | \(2863288/13286025\) | \(-800300828275200\) | \([2]\) | \(110592\) | \(1.5386\) | |
23520.n2 | 23520l3 | \([0, -1, 0, -24320, -804600]\) | \(26410345352/10546875\) | \(635304600000000\) | \([2]\) | \(110592\) | \(1.5386\) | |
23520.n1 | 23520l4 | \([0, -1, 0, -176465, 28591137]\) | \(1261112198464/675\) | \(325275955200\) | \([2]\) | \(110592\) | \(1.5386\) |
Rank
sage: E.rank()
The elliptic curves in class 23520l have rank \(1\).
Complex multiplication
The elliptic curves in class 23520l do not have complex multiplication.Modular form 23520.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.