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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 74970.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74970.o1 | 74970n2 | \([1, -1, 0, -2928690, -1990582700]\) | \(-32391289681150609/1228250000000\) | \(-105342238118250000000\) | \([]\) | \(2721600\) | \(2.6120\) | |
74970.o2 | 74970n1 | \([1, -1, 0, 175950, -8862764]\) | \(7023836099951/4456448000\) | \(-382212258398208000\) | \([]\) | \(907200\) | \(2.0627\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74970.o have rank \(1\).
Complex multiplication
The elliptic curves in class 74970.o do not have complex multiplication.Modular form 74970.2.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.