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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 407330.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
407330.o1 | 407330o2 | \([1, 1, 0, -38892, 2933546]\) | \(43949604889/42350\) | \(6269319899150\) | \([2]\) | \(1520640\) | \(1.3767\) | \(\Gamma_0(N)\)-optimal* |
407330.o2 | 407330o1 | \([1, 1, 0, -1862, 67424]\) | \(-4826809/10780\) | \(-1595826883420\) | \([2]\) | \(760320\) | \(1.0302\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 407330.o have rank \(0\).
Complex multiplication
The elliptic curves in class 407330.o do not have complex multiplication.Modular form 407330.2.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 LMFDB 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 LMFDB labels.