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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 320790c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
320790.c2 | 320790c1 | \([1, 1, 0, -61928, 5948928]\) | \(-5346247607800793/44979864000\) | \(-220986071832000\) | \([2]\) | \(2377728\) | \(1.5783\) | \(\Gamma_0(N)\)-optimal |
320790.c1 | 320790c2 | \([1, 1, 0, -992848, 380364952]\) | \(22030579815938993753/1540125000\) | \(7566634125000\) | \([2]\) | \(4755456\) | \(1.9249\) |
Rank
sage: E.rank()
The elliptic curves in class 320790c have rank \(0\).
Complex multiplication
The elliptic curves in class 320790c do not have complex multiplication.Modular form 320790.2.a.c
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.