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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 69696.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69696.o1 | 69696bg2 | \([0, 0, 0, -48972, -125840]\) | \(102129622/59049\) | \(7509794573647872\) | \([2]\) | \(737280\) | \(1.7357\) | |
69696.o2 | 69696bg1 | \([0, 0, 0, -33132, 2313520]\) | \(63253004/243\) | \(15452252209152\) | \([2]\) | \(368640\) | \(1.3892\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69696.o have rank \(0\).
Complex multiplication
The elliptic curves in class 69696.o do not have complex multiplication.Modular form 69696.2.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.