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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 27797b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27797.b2 | 27797b1 | \([1, 0, 0, 1256, -64905]\) | \(4657463/41503\) | \(-1952545199143\) | \([2]\) | \(43200\) | \(1.0396\) | \(\Gamma_0(N)\)-optimal |
27797.b1 | 27797b2 | \([1, 0, 0, -18599, -902786]\) | \(15124197817/1294139\) | \(60883909391459\) | \([2]\) | \(86400\) | \(1.3862\) |
Rank
sage: E.rank()
The elliptic curves in class 27797b have rank \(1\).
Complex multiplication
The elliptic curves in class 27797b do not have complex multiplication.Modular form 27797.2.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.