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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 57330c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.o3 | 57330c1 | \([1, -1, 0, -12210, -521984]\) | \(-63378025803/812500\) | \(-2580924937500\) | \([2]\) | \(165888\) | \(1.1909\) | \(\Gamma_0(N)\)-optimal |
57330.o2 | 57330c2 | \([1, -1, 0, -195960, -33339734]\) | \(261984288445803/42250\) | \(134208096750\) | \([2]\) | \(331776\) | \(1.5375\) | |
57330.o4 | 57330c3 | \([1, -1, 0, 42915, -2681659]\) | \(3774555693/3515200\) | \(-8140096850558400\) | \([2]\) | \(497664\) | \(1.7402\) | |
57330.o1 | 57330c4 | \([1, -1, 0, -221685, -24008419]\) | \(520300455507/193072360\) | \(447094819516920120\) | \([2]\) | \(995328\) | \(2.0868\) |
Rank
sage: E.rank()
The elliptic curves in class 57330c have rank \(0\).
Complex multiplication
The elliptic curves in class 57330c do not have complex multiplication.Modular form 57330.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.