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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 35280.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.cv1 | 35280el4 | \([0, 0, 0, -1888803, 999095202]\) | \(2121328796049/120050\) | \(42173328695500800\) | \([2]\) | \(589824\) | \(2.2544\) | |
35280.cv2 | 35280el3 | \([0, 0, 0, -618723, -175051422]\) | \(74565301329/5468750\) | \(1921161110400000000\) | \([2]\) | \(589824\) | \(2.2544\) | |
35280.cv3 | 35280el2 | \([0, 0, 0, -124803, 13724802]\) | \(611960049/122500\) | \(43034008872960000\) | \([2, 2]\) | \(294912\) | \(1.9078\) | |
35280.cv4 | 35280el1 | \([0, 0, 0, 16317, 1278018]\) | \(1367631/2800\) | \(-983634488524800\) | \([2]\) | \(147456\) | \(1.5612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.cv do not have complex multiplication.Modular form 35280.2.a.cv
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.