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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 18810.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18810.o1 | 18810o2 | \([1, -1, 1, -5602988, 5106187567]\) | \(988305981822719034363/14242764800\) | \(280340339558400\) | \([2]\) | \(557568\) | \(2.3249\) | |
18810.o2 | 18810o1 | \([1, -1, 1, -349868, 80002351]\) | \(-240626759839351803/916056965120\) | \(-18030749244456960\) | \([2]\) | \(278784\) | \(1.9783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18810.o have rank \(1\).
Complex multiplication
The elliptic curves in class 18810.o do not have complex multiplication.Modular form 18810.2.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.