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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 162288n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162288.be2 | 162288n1 | \([0, 0, 0, -57771, -24875046]\) | \(-60698457/725788\) | \(-254967895770513408\) | \([2]\) | \(1769472\) | \(2.0218\) | \(\Gamma_0(N)\)-optimal |
162288.be1 | 162288n2 | \([0, 0, 0, -1680651, -835990470]\) | \(1494447319737/5411854\) | \(1901173657593176064\) | \([2]\) | \(3538944\) | \(2.3684\) |
Rank
sage: E.rank()
The elliptic curves in class 162288n have rank \(1\).
Complex multiplication
The elliptic curves in class 162288n do not have complex multiplication.Modular form 162288.2.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.