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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 32760.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32760.g1 | 32760w2 | \([0, 0, 0, -7803, -263898]\) | \(2606857452/15925\) | \(320974617600\) | \([2]\) | \(43008\) | \(1.0466\) | |
32760.g2 | 32760w1 | \([0, 0, 0, -783, 1458]\) | \(10536048/5915\) | \(29804785920\) | \([2]\) | \(21504\) | \(0.69998\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32760.g have rank \(1\).
Complex multiplication
The elliptic curves in class 32760.g do not have complex multiplication.Modular form 32760.2.a.g
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.