Show commands:
SageMath
E = EllipticCurve("bpr1")
E.isogeny_class()
Elliptic curves in class 6350400.bpr
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
6350400.bpr1 | \([0, 0, 0, -17654700, 28675486000]\) | \(-15590912409/78125\) | \(-3049462080000000000000\) | \([]\) | \(340623360\) | \(2.9698\) |
6350400.bpr2 | \([0, 0, 0, -14700, -21266000]\) | \(-9/5\) | \(-195165573120000000\) | \([]\) | \(48660480\) | \(1.9968\) |
Rank
sage: E.rank()
The elliptic curves in class 6350400.bpr have rank \(0\).
Complex multiplication
The elliptic curves in class 6350400.bpr do not have complex multiplication.Modular form 6350400.2.a.bpr
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.