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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 87616.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87616.p1 | 87616j3 | \([0, -1, 0, -10258373, -12642949961]\) | \(727057727488000/37\) | \(6075640136512\) | \([]\) | \(1181952\) | \(2.3741\) | |
87616.p2 | 87616j2 | \([0, -1, 0, -127773, -16980569]\) | \(1404928000/50653\) | \(8317551346884928\) | \([]\) | \(393984\) | \(1.8248\) | |
87616.p3 | 87616j1 | \([0, -1, 0, -18253, 947855]\) | \(4096000/37\) | \(6075640136512\) | \([]\) | \(131328\) | \(1.2755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87616.p have rank \(1\).
Complex multiplication
The elliptic curves in class 87616.p do not have complex multiplication.Modular form 87616.2.a.p
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.