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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 1274.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1274.o1 | 1274n2 | \([1, -1, 1, -10422, 451903]\) | \(-1064019559329/125497034\) | \(-14764600553066\) | \([]\) | \(5292\) | \(1.2627\) | |
1274.o2 | 1274n1 | \([1, -1, 1, -132, -857]\) | \(-2146689/1664\) | \(-195767936\) | \([]\) | \(756\) | \(0.28979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1274.o have rank \(0\).
Complex multiplication
The elliptic curves in class 1274.o do not have complex multiplication.Modular form 1274.2.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.