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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 15680n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.cd1 | 15680n1 | \([0, 1, 0, -195281, -33300625]\) | \(-177953104/125\) | \(-578509309952000\) | \([]\) | \(96768\) | \(1.7689\) | \(\Gamma_0(N)\)-optimal |
15680.cd2 | 15680n2 | \([0, 1, 0, 188879, -141095921]\) | \(161017136/1953125\) | \(-9039207968000000000\) | \([]\) | \(290304\) | \(2.3182\) |
Rank
sage: E.rank()
The elliptic curves in class 15680n have rank \(0\).
Complex multiplication
The elliptic curves in class 15680n do not have complex multiplication.Modular form 15680.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.