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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 199056.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 199056.o1 | 199056br2 | \([0, -1, 0, -2608738096, 51286299668032]\) | \(-479352730263827621784814619569/214316023050990383094\) | \(-877838430416856609153024\) | \([]\) | \(81134592\) | \(3.9347\) | |
| 199056.o2 | 199056br1 | \([0, -1, 0, 6588464, -528047168]\) | \(7721758769769063671471/4497774542859970944\) | \(-18422884527554440986624\) | \([]\) | \(11590656\) | \(2.9618\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 199056.o have rank \(1\).
Complex multiplication
The elliptic curves in class 199056.o do not have complex multiplication.Modular form 199056.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
