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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 152460.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.q1 | 152460bs2 | \([0, 0, 0, -3917133, -2984172543]\) | \(-98463644928/6125\) | \(-413484133762854000\) | \([]\) | \(3421440\) | \(2.4396\) | |
| 152460.q2 | 152460bs1 | \([0, 0, 0, -3993, -11229647]\) | \(-76032/588245\) | \(-54473273260061040\) | \([3]\) | \(1140480\) | \(1.8903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.q have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.q do not have complex multiplication.Modular form 152460.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
