Properties

Label 7600.c
Number of curves $3$
Conductor $7600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 7600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.c1 7600m3 \([0, 1, 0, -307733, 65604163]\) \(-50357871050752/19\) \(-1216000000\) \([]\) \(23328\) \(1.5313\)  
7600.c2 7600m2 \([0, 1, 0, -3733, 92163]\) \(-89915392/6859\) \(-438976000000\) \([]\) \(7776\) \(0.98200\)  
7600.c3 7600m1 \([0, 1, 0, 267, 163]\) \(32768/19\) \(-1216000000\) \([]\) \(2592\) \(0.43269\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7600.c have rank \(0\).

Complex multiplication

The elliptic curves in class 7600.c do not have complex multiplication.

Modular form 7600.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{7} + q^{9} - 3q^{11} + 4q^{13} + 3q^{17} - q^{19} + O(q^{20})\)  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.