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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 75088.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75088.b1 | 75088bj2 | \([0, 0, 0, -1228483, -575017406]\) | \(-1064019559329/125497034\) | \(-24183269488299843584\) | \([]\) | \(2201472\) | \(2.4552\) | |
| 75088.b2 | 75088bj1 | \([0, 0, 0, -15523, 1138594]\) | \(-2146689/1664\) | \(-320652681150464\) | \([]\) | \(314496\) | \(1.4822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75088.b have rank \(2\).
Complex multiplication
The elliptic curves in class 75088.b do not have complex multiplication.Modular form 75088.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
