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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 51600cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.cl2 | 51600cu1 | \([0, 1, 0, -15008, -480012]\) | \(5841725401/1857600\) | \(118886400000000\) | \([2]\) | \(165888\) | \(1.4046\) | \(\Gamma_0(N)\)-optimal |
51600.cl1 | 51600cu2 | \([0, 1, 0, -95008, 10879988]\) | \(1481933914201/53916840\) | \(3450677760000000\) | \([2]\) | \(331776\) | \(1.7512\) |
Rank
sage: E.rank()
The elliptic curves in class 51600cu have rank \(1\).
Complex multiplication
The elliptic curves in class 51600cu do not have complex multiplication.Modular form 51600.2.a.cu
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.