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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 374790.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374790.o1 | 374790o2 | \([1, 1, 0, -844258, -298126508]\) | \(74985951512809/233868960\) | \(207559562871641760\) | \([2]\) | \(8601600\) | \(2.1904\) | |
374790.o2 | 374790o1 | \([1, 1, 0, -75458, -293388]\) | \(53540005609/30950400\) | \(27468593928422400\) | \([2]\) | \(4300800\) | \(1.8438\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374790.o have rank \(1\).
Complex multiplication
The elliptic curves in class 374790.o do not have complex multiplication.Modular form 374790.2.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.