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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 257754.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.o1 | 257754o2 | \([1, 1, 0, -1000699, -274235105]\) | \(343441189027/98375634\) | \(31744606853009516886\) | \([2]\) | \(8147200\) | \(2.4485\) | |
257754.o2 | 257754o1 | \([1, 1, 0, 165331, -28202775]\) | \(1548816893/1966356\) | \(-634518890653923324\) | \([2]\) | \(4073600\) | \(2.1020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257754.o have rank \(0\).
Complex multiplication
The elliptic curves in class 257754.o do not have complex multiplication.Modular form 257754.2.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.