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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 44506.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44506.b1 | 44506i2 | \([1, 0, 1, -67777, -6797160]\) | \(1426487591593/2156\) | \(52040598764\) | \([2]\) | \(165888\) | \(1.3243\) | |
44506.b2 | 44506i1 | \([1, 0, 1, -4197, -108544]\) | \(-338608873/13552\) | \(-327112335088\) | \([2]\) | \(82944\) | \(0.97772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44506.b have rank \(0\).
Complex multiplication
The elliptic curves in class 44506.b do not have complex multiplication.Modular form 44506.2.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.