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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 57222br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57222.bv2 | 57222br1 | \([1, -1, 1, -7731159134, 261228419657453]\) | \(591139158854005457801/1097587482427392\) | \(94887054663038733073772445696\) | \([2]\) | \(111132672\) | \(4.4510\) | \(\Gamma_0(N)\)-optimal |
57222.bv1 | 57222br2 | \([1, -1, 1, -123643371614, 16734208408465133]\) | \(2418067440128989194388361/8359273562112\) | \(722663897074725458457133056\) | \([2]\) | \(222265344\) | \(4.7975\) |
Rank
sage: E.rank()
The elliptic curves in class 57222br have rank \(0\).
Complex multiplication
The elliptic curves in class 57222br do not have complex multiplication.Modular form 57222.2.a.br
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.