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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 14490.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.c1 | 14490f3 | \([1, -1, 0, -1622880, -795346394]\) | \(648418741232906810881/33810\) | \(24647490\) | \([2]\) | \(98304\) | \(1.8117\) | |
14490.c2 | 14490f4 | \([1, -1, 0, -103500, -11873750]\) | \(168197522113656001/13424780328750\) | \(9786664859658750\) | \([2]\) | \(98304\) | \(1.8117\) | |
14490.c3 | 14490f2 | \([1, -1, 0, -101430, -12408224]\) | \(158306179791523681/1143116100\) | \(833331636900\) | \([2, 2]\) | \(49152\) | \(1.4651\) | |
14490.c4 | 14490f1 | \([1, -1, 0, -6210, -201020]\) | \(-36333758230561/3290930160\) | \(-2399088086640\) | \([2]\) | \(24576\) | \(1.1186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14490.c have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.c do not have complex multiplication.Modular form 14490.2.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.