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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 363090.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363090.b1 | 363090b2 | \([1, 1, 0, -1348848, 584975952]\) | \(2306880043867559161/76058277750000\) | \(8948180319009750000\) | \([2]\) | \(12386304\) | \(2.4097\) | |
363090.b2 | 363090b1 | \([1, 1, 0, 27072, 31580928]\) | \(18649681956359/3670404192000\) | \(-431819382784608000\) | \([2]\) | \(6193152\) | \(2.0631\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363090.b have rank \(1\).
Complex multiplication
The elliptic curves in class 363090.b do not have complex multiplication.Modular form 363090.2.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.