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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 39600.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.c1 | 39600v4 | \([0, 0, 0, -270075, 53932250]\) | \(186779563204/360855\) | \(4209012720000000\) | \([2]\) | \(393216\) | \(1.8869\) | |
39600.c2 | 39600v3 | \([0, 0, 0, -225075, -40882750]\) | \(108108036004/658845\) | \(7684768080000000\) | \([2]\) | \(393216\) | \(1.8869\) | |
39600.c3 | 39600v2 | \([0, 0, 0, -22575, 224750]\) | \(436334416/245025\) | \(714492900000000\) | \([2, 2]\) | \(196608\) | \(1.5404\) | |
39600.c4 | 39600v1 | \([0, 0, 0, 5550, 27875]\) | \(103737344/61875\) | \(-11276718750000\) | \([2]\) | \(98304\) | \(1.1938\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.c have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.c do not have complex multiplication.Modular form 39600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.