Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 705600.bw
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.bw1 | \([0, 0, 0, -3807300, 67228000]\) | \(3241792/1875\) | \(3530133540360000000000\) | \([2]\) | \(44040192\) | \(2.8241\) |
705600.bw2 | \([0, 0, 0, -2649675, 1655489500]\) | \(69934528/225\) | \(6619000388175000000\) | \([2]\) | \(22020096\) | \(2.4775\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bw do not have complex multiplication.Modular form 705600.2.a.bw
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.