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Properties

Label 8450.c
Number of curves $3$
Conductor $8450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 8450.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8450.c1 8450c3 \([1, 1, 0, -1941475, -1042037875]\) \(-10730978619193/6656\) \(-501988136000000\) \([]\) \(108864\) \(2.1416\)  
8450.c2 8450c2 \([1, 1, 0, -19100, -2033000]\) \(-10218313/17576\) \(-1325562421625000\) \([]\) \(36288\) \(1.5923\)  
8450.c3 8450c1 \([1, 1, 0, 2025, 58375]\) \(12167/26\) \(-1960891156250\) \([]\) \(12096\) \(1.0430\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8450.c have rank \(1\).

Complex multiplication

The elliptic curves in class 8450.c do not have complex multiplication.

Modular form 8450.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} - 2 q^{9} - 6 q^{11} - q^{12} + q^{14} + q^{16} + 3 q^{17} + 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.