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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 212940.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212940.b1 | 212940bw2 | \([0, 0, 0, -1008423, 20049822]\) | \(2122416/1225\) | \(65457214059386822400\) | \([2]\) | \(5391360\) | \(2.4919\) | |
| 212940.b2 | 212940bw1 | \([0, 0, 0, -711828, 230572953]\) | \(11943936/35\) | \(116887882248905040\) | \([2]\) | \(2695680\) | \(2.1453\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212940.b have rank \(1\).
Complex multiplication
The elliptic curves in class 212940.b do not have complex multiplication.Modular form 212940.2.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.
