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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2100.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2100.q1 | 2100m1 | \([0, 1, 0, -101533, 8245688]\) | \(463030539649024/149501953125\) | \(37375488281250000\) | \([2]\) | \(20160\) | \(1.8834\) | \(\Gamma_0(N)\)-optimal |
2100.q2 | 2100m2 | \([0, 1, 0, 289092, 56683188]\) | \(667990736021936/732392128125\) | \(-2929568512500000000\) | \([2]\) | \(40320\) | \(2.2300\) |
Rank
sage: E.rank()
The elliptic curves in class 2100.q have rank \(0\).
Complex multiplication
The elliptic curves in class 2100.q do not have complex multiplication.Modular form 2100.2.a.q
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.