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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 95370b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.e2 | 95370b1 | \([1, 1, 0, -2173, 1369213]\) | \(-47045881/33570240\) | \(-810303984346560\) | \([2]\) | \(663552\) | \(1.5398\) | \(\Gamma_0(N)\)-optimal |
95370.e1 | 95370b2 | \([1, 1, 0, -198693, 33637797]\) | \(35940267099001/448014600\) | \(10813983320507400\) | \([2]\) | \(1327104\) | \(1.8863\) |
Rank
sage: E.rank()
The elliptic curves in class 95370b have rank \(1\).
Complex multiplication
The elliptic curves in class 95370b do not have complex multiplication.Modular form 95370.2.a.b
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.