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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 123840.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.b1 | 123840cj2 | \([0, 0, 0, -95486988, 359139964912]\) | \(503835593418244309249/898614000000\) | \(171727809675264000000\) | \([2]\) | \(15482880\) | \(3.1410\) | |
123840.b2 | 123840cj1 | \([0, 0, 0, -5907468, 5730842608]\) | \(-119305480789133569/5200091136000\) | \(-993752891560820736000\) | \([2]\) | \(7741440\) | \(2.7944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 123840.b have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.b do not have complex multiplication.Modular form 123840.2.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.