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SageMath
E = EllipticCurve("bpa1")
E.isogeny_class()
Elliptic curves in class 6350400.bpa
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
6350400.bpa1 | \([0, 0, 0, -158892300, 774238122000]\) | \(-15590912409/78125\) | \(-2223057856320000000000000\) | \([]\) | \(1021870080\) | \(3.5191\) |
6350400.bpa2 | \([0, 0, 0, -132300, -574182000]\) | \(-9/5\) | \(-142275702804480000000\) | \([]\) | \(145981440\) | \(2.5461\) |
Rank
sage: E.rank()
The elliptic curves in class 6350400.bpa have rank \(0\).
Complex multiplication
The elliptic curves in class 6350400.bpa do not have complex multiplication.Modular form 6350400.2.a.bpa
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.