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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1760n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1760.m2 | 1760n1 | \([0, -1, 0, -4170, -102268]\) | \(125330290485184/378125\) | \(24200000\) | \([2]\) | \(960\) | \(0.64455\) | \(\Gamma_0(N)\)-optimal |
1760.m1 | 1760n2 | \([0, -1, 0, -4225, -99375]\) | \(2036792051776/107421875\) | \(440000000000\) | \([2]\) | \(1920\) | \(0.99112\) |
Rank
sage: E.rank()
The elliptic curves in class 1760n have rank \(0\).
Complex multiplication
The elliptic curves in class 1760n do not have complex multiplication.Modular form 1760.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.