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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 7920.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.i1 | 7920y4 | \([0, 0, 0, -8523, 302778]\) | \(22930509321/6875\) | \(20528640000\) | \([2]\) | \(8192\) | \(0.95679\) | |
7920.i2 | 7920y3 | \([0, 0, 0, -4203, -102438]\) | \(2749884201/73205\) | \(218588958720\) | \([2]\) | \(8192\) | \(0.95679\) | |
7920.i3 | 7920y2 | \([0, 0, 0, -603, 3402]\) | \(8120601/3025\) | \(9032601600\) | \([2, 2]\) | \(4096\) | \(0.61021\) | |
7920.i4 | 7920y1 | \([0, 0, 0, 117, 378]\) | \(59319/55\) | \(-164229120\) | \([2]\) | \(2048\) | \(0.26364\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7920.i have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.i do not have complex multiplication.Modular form 7920.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.