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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 7488.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7488.o1 | 7488c1 | \([0, 0, 0, -51, 140]\) | \(8489664/13\) | \(22464\) | \([2]\) | \(512\) | \(-0.26546\) | \(\Gamma_0(N)\)-optimal |
7488.o2 | 7488c2 | \([0, 0, 0, -36, 224]\) | \(-46656/169\) | \(-18690048\) | \([2]\) | \(1024\) | \(0.081110\) |
Rank
sage: E.rank()
The elliptic curves in class 7488.o have rank \(1\).
Complex multiplication
The elliptic curves in class 7488.o do not have complex multiplication.Modular form 7488.2.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.