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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 55545.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55545.o1 | 55545j1 | \([0, 1, 1, -1711491, 861368285]\) | \(-7079867613184/1250235\) | \(-97907134682791035\) | \([3]\) | \(715392\) | \(2.2651\) | \(\Gamma_0(N)\)-optimal |
| 55545.o2 | 55545j2 | \([0, 1, 1, 478569, 2866039706]\) | \(154786758656/45397807875\) | \(-3555147064288790887875\) | \([]\) | \(2146176\) | \(2.8144\) |
Rank
sage: E.rank()
The elliptic curves in class 55545.o have rank \(0\).
Complex multiplication
The elliptic curves in class 55545.o do not have complex multiplication.Modular form 55545.2.a.o
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.
