Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 10010.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10010.b1 | 10010h2 | \([1, 0, 1, -463, 2538]\) | \(10942526586601/3464060600\) | \(3464060600\) | \([2]\) | \(7680\) | \(0.53442\) | |
10010.b2 | 10010h1 | \([1, 0, 1, -183, -934]\) | \(672451615081/24664640\) | \(24664640\) | \([2]\) | \(3840\) | \(0.18785\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10010.b have rank \(1\).
Complex multiplication
The elliptic curves in class 10010.b do not have complex multiplication.Modular form 10010.2.a.b
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.