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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 45864b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45864.cd1 | 45864b1 | \([0, 0, 0, -4263, 106330]\) | \(10536048/91\) | \(74000279808\) | \([2]\) | \(86016\) | \(0.90999\) | \(\Gamma_0(N)\)-optimal |
45864.cd2 | 45864b2 | \([0, 0, 0, -1323, 250390]\) | \(-78732/8281\) | \(-26936101850112\) | \([2]\) | \(172032\) | \(1.2566\) |
Rank
sage: E.rank()
The elliptic curves in class 45864b have rank \(0\).
Complex multiplication
The elliptic curves in class 45864b do not have complex multiplication.Modular form 45864.2.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 Cremona 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 Cremona labels.