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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 95370.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.ba1 | 95370bf2 | \([1, 0, 1, -53668029, -151333263848]\) | \(708234550511150304361/23696640000\) | \(571979283068160000\) | \([2]\) | \(8110080\) | \(2.9069\) | |
95370.ba2 | 95370bf1 | \([1, 0, 1, -3358909, -2357897704]\) | \(173629978755828841/1000026931200\) | \(24138219053698252800\) | \([2]\) | \(4055040\) | \(2.5603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 95370.ba do not have complex multiplication.Modular form 95370.2.a.ba
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.