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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 32760g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32760.c2 | 32760g1 | \([0, 0, 0, -363, -1258]\) | \(7086244/3185\) | \(2377589760\) | \([2]\) | \(15360\) | \(0.49444\) | \(\Gamma_0(N)\)-optimal |
32760.c1 | 32760g2 | \([0, 0, 0, -2883, 58718]\) | \(1775007362/29575\) | \(44155238400\) | \([2]\) | \(30720\) | \(0.84101\) |
Rank
sage: E.rank()
The elliptic curves in class 32760g have rank \(0\).
Complex multiplication
The elliptic curves in class 32760g 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 Cremona 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 Cremona labels.