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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7920.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.p1 | 7920f4 | \([0, 0, 0, -10803, 431458]\) | \(186779563204/360855\) | \(269376814080\) | \([2]\) | \(16384\) | \(1.0822\) | |
7920.p2 | 7920f3 | \([0, 0, 0, -9003, -327062]\) | \(108108036004/658845\) | \(491825157120\) | \([2]\) | \(16384\) | \(1.0822\) | |
7920.p3 | 7920f2 | \([0, 0, 0, -903, 1798]\) | \(436334416/245025\) | \(45727545600\) | \([2, 2]\) | \(8192\) | \(0.73565\) | |
7920.p4 | 7920f1 | \([0, 0, 0, 222, 223]\) | \(103737344/61875\) | \(-721710000\) | \([2]\) | \(4096\) | \(0.38907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7920.p have rank \(0\).
Complex multiplication
The elliptic curves in class 7920.p do not have complex multiplication.Modular form 7920.2.a.p
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.