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Properties

Label 7650x
Number of curves $2$
Conductor $7650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 7650x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7650.k2 7650x1 \([1, -1, 0, -601542, -232423884]\) \(-2113364608155289/828431400960\) \(-9436351426560000000\) \([2]\) \(193536\) \(2.3501\) \(\Gamma_0(N)\)-optimal
7650.k1 7650x2 \([1, -1, 0, -10393542, -12893479884]\) \(10901014250685308569/1040774054400\) \(11855066963400000000\) \([2]\) \(387072\) \(2.6966\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7650x have rank \(1\).

Complex multiplication

The elliptic curves in class 7650x do not have complex multiplication.

Modular form 7650.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} + 4 q^{11} - 4 q^{13} + 2 q^{14} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.