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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3610.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3610.b1 | 3610e2 | \([1, 1, 0, -1003587, 386555179]\) | \(-2376117230685121/342950\) | \(-16134384888950\) | \([]\) | \(25920\) | \(1.9434\) | |
3610.b2 | 3610e1 | \([1, 1, 0, -10837, 664229]\) | \(-2992209121/2375000\) | \(-111733967375000\) | \([]\) | \(8640\) | \(1.3941\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3610.b have rank \(1\).
Complex multiplication
The elliptic curves in class 3610.b do not have complex multiplication.Modular form 3610.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.