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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 15675.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15675.o1 | 15675j2 | \([0, -1, 1, -751583, -250541557]\) | \(-3004935183806464000/2037123\) | \(-31830046875\) | \([]\) | \(77760\) | \(1.7649\) | |
15675.o2 | 15675j1 | \([0, -1, 1, -9083, -356182]\) | \(-5304438784000/497763387\) | \(-7777552921875\) | \([]\) | \(25920\) | \(1.2156\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15675.o have rank \(1\).
Complex multiplication
The elliptic curves in class 15675.o do not have complex multiplication.Modular form 15675.2.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.