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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 95370.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.bi1 | 95370bo1 | \([1, 0, 1, -25583, -1334482]\) | \(76711450249/12622500\) | \(304676464702500\) | \([2]\) | \(552960\) | \(1.5008\) | \(\Gamma_0(N)\)-optimal |
95370.bi2 | 95370bo2 | \([1, 0, 1, 46667, -7490182]\) | \(465664585751/1274620050\) | \(-30766229405658450\) | \([2]\) | \(1105920\) | \(1.8473\) |
Rank
sage: E.rank()
The elliptic curves in class 95370.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 95370.bi do not have complex multiplication.Modular form 95370.2.a.bi
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.