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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 309168.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309168.b1 | 309168b1 | \([0, 0, 0, -21764187, -39003270390]\) | \(14141641322151794907/32376123526144\) | \(2610213844439418273792\) | \([2]\) | \(22118400\) | \(2.9908\) | \(\Gamma_0(N)\)-optimal |
309168.b2 | 309168b2 | \([0, 0, 0, -13953627, -67379034870]\) | \(-3726780377767300827/22169935588208416\) | \(-1787374969580364808716288\) | \([2]\) | \(44236800\) | \(3.3373\) |
Rank
sage: E.rank()
The elliptic curves in class 309168.b have rank \(1\).
Complex multiplication
The elliptic curves in class 309168.b do not have complex multiplication.Modular form 309168.2.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.