Properties

Label 7600.m
Number of curves $2$
Conductor $7600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7600.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.m1 7600k2 \([0, 1, 0, -1112008, 450975988]\) \(-2376117230685121/342950\) \(-21948800000000\) \([]\) \(41472\) \(1.9690\)  
7600.m2 7600k1 \([0, 1, 0, -12008, 775988]\) \(-2992209121/2375000\) \(-152000000000000\) \([]\) \(13824\) \(1.4197\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7600.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.