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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 98736o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.v1 | 98736o1 | \([0, -1, 0, -158308, 24271744]\) | \(967473250000/1153977\) | \(523351205912832\) | \([2]\) | \(460800\) | \(1.7354\) | \(\Gamma_0(N)\)-optimal |
98736.v2 | 98736o2 | \([0, -1, 0, -117168, 37140336]\) | \(-98061470500/271048833\) | \(-491703850637632512\) | \([2]\) | \(921600\) | \(2.0820\) |
Rank
sage: E.rank()
The elliptic curves in class 98736o have rank \(1\).
Complex multiplication
The elliptic curves in class 98736o do not have complex multiplication.Modular form 98736.2.a.o
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.