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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 36100.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36100.b1 | 36100c2 | \([0, 1, 0, -12508, 533988]\) | \(7888624/5\) | \(137180000000\) | \([2]\) | \(46080\) | \(1.0782\) | |
36100.b2 | 36100c1 | \([0, 1, 0, -633, 11488]\) | \(-16384/25\) | \(-42868750000\) | \([2]\) | \(23040\) | \(0.73167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36100.b have rank \(2\).
Complex multiplication
The elliptic curves in class 36100.b do not have complex multiplication.Modular form 36100.2.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.