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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 7600.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7600.e1 | 7600i2 | \([0, 1, 0, -9628, -366852]\) | \(3084800518928/361\) | \(11552000\) | \([2]\) | \(7168\) | \(0.77709\) | |
7600.e2 | 7600i1 | \([0, 1, 0, -603, -5852]\) | \(12144109568/130321\) | \(260642000\) | \([2]\) | \(3584\) | \(0.43052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7600.e have rank \(1\).
Complex multiplication
The elliptic curves in class 7600.e do not have complex multiplication.Modular form 7600.2.a.e
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.