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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7920.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.c1 | 7920j3 | \([0, 0, 0, -95043, -11277902]\) | \(127191074376964/495\) | \(369515520\) | \([2]\) | \(16384\) | \(1.2801\) | |
7920.c2 | 7920j2 | \([0, 0, 0, -5943, -176042]\) | \(124386546256/245025\) | \(45727545600\) | \([2, 2]\) | \(8192\) | \(0.93355\) | |
7920.c3 | 7920j4 | \([0, 0, 0, -3963, -295238]\) | \(-9220796644/45106875\) | \(-33672101760000\) | \([2]\) | \(16384\) | \(1.2801\) | |
7920.c4 | 7920j1 | \([0, 0, 0, -498, -713]\) | \(1171019776/658845\) | \(7684768080\) | \([2]\) | \(4096\) | \(0.58698\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7920.c have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.c do not have complex multiplication.Modular form 7920.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.