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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 212940bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212940.m2 | 212940bj1 | \([0, 0, 0, 312, 6253]\) | \(131072/735\) | \(-18834968880\) | \([2]\) | \(119808\) | \(0.65360\) | \(\Gamma_0(N)\)-optimal |
212940.m1 | 212940bj2 | \([0, 0, 0, -3783, 80782]\) | \(14602768/1575\) | \(645770361600\) | \([2]\) | \(239616\) | \(1.0002\) |
Rank
sage: E.rank()
The elliptic curves in class 212940bj have rank \(0\).
Complex multiplication
The elliptic curves in class 212940bj do not have complex multiplication.Modular form 212940.2.a.bj
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.