Properties

Label 7600.r
Number of curves $2$
Conductor $7600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7600.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.r1 7600q1 \([0, -1, 0, -23033, -1247188]\) \(5405726654464/407253125\) \(101813281250000\) \([2]\) \(23040\) \(1.4331\) \(\Gamma_0(N)\)-optimal
7600.r2 7600q2 \([0, -1, 0, 22092, -5579188]\) \(298091207216/3525390625\) \(-14101562500000000\) \([2]\) \(46080\) \(1.7797\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7600.r have rank \(1\).

Complex multiplication

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

Modular form 7600.2.a.r

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + 2q^{7} + q^{9} - 6q^{13} - 2q^{17} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.