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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 254100.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.b1 | 254100b2 | \([0, -1, 0, -29246708, 60887901912]\) | \(3123406998416/17787\) | \(15755377753500000000\) | \([2]\) | \(21196800\) | \(2.8749\) | |
254100.b2 | 254100b1 | \([0, -1, 0, -1794833, 987910662]\) | \(-11550212096/922383\) | \(-51064304683218750000\) | \([2]\) | \(10598400\) | \(2.5283\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.b have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.b do not have complex multiplication.Modular form 254100.2.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.