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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 36100b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36100.h2 | 36100b1 | \([0, -1, 0, -228633, -80167738]\) | \(-16384/25\) | \(-2016798111118750000\) | \([2]\) | \(437760\) | \(2.2039\) | \(\Gamma_0(N)\)-optimal |
36100.h1 | 36100b2 | \([0, -1, 0, -4515508, -3689716488]\) | \(7888624/5\) | \(6453753955580000000\) | \([2]\) | \(875520\) | \(2.5505\) |
Rank
sage: E.rank()
The elliptic curves in class 36100b have rank \(0\).
Complex multiplication
The elliptic curves in class 36100b 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 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.