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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8712.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8712.o1 | 8712c2 | \([0, 0, 0, -9075, 311454]\) | \(1687500/121\) | \(5926594341888\) | \([2]\) | \(15360\) | \(1.1977\) | |
| 8712.o2 | 8712c1 | \([0, 0, 0, -1815, -23958]\) | \(54000/11\) | \(134695325952\) | \([2]\) | \(7680\) | \(0.85113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8712.o have rank \(0\).
Complex multiplication
The elliptic curves in class 8712.o do not have complex multiplication.Modular form 8712.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
