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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1920.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1920.b1 | 1920l2 | \([0, -1, 0, -33321, -2330055]\) | \(499460194376672/253125\) | \(2073600000\) | \([2]\) | \(3840\) | \(1.1206\) | |
| 1920.b2 | 1920l1 | \([0, -1, 0, -2071, -36305]\) | \(-3839138053504/87890625\) | \(-22500000000\) | \([2]\) | \(1920\) | \(0.77401\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1920.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1920.b do not have complex multiplication.Modular form 1920.2.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.
