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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 88935.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.v1 | 88935ci4 | \([1, 0, 0, -12590355, -17010223350]\) | \(1058993490188089/13182390375\) | \(2747505177219825243375\) | \([2]\) | \(6635520\) | \(2.9235\) | |
88935.v2 | 88935ci2 | \([1, 0, 0, -1473480, 267623775]\) | \(1697509118089/833765625\) | \(173775415998892640625\) | \([2, 2]\) | \(3317760\) | \(2.5769\) | |
88935.v3 | 88935ci1 | \([1, 0, 0, -1206675, 509722632]\) | \(932288503609/779625\) | \(162491298076886625\) | \([4]\) | \(1658880\) | \(2.2304\) | \(\Gamma_0(N)\)-optimal |
88935.v4 | 88935ci3 | \([1, 0, 0, 5374515, 2052211272]\) | \(82375335041831/56396484375\) | \(-11754289502089599609375\) | \([2]\) | \(6635520\) | \(2.9235\) |
Rank
sage: E.rank()
The elliptic curves in class 88935.v have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.v do not have complex multiplication.Modular form 88935.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.