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Properties

Label 7605.q
Number of curves $2$
Conductor $7605$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 7605.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7605.q1 7605f2 \([1, -1, 0, -607164, 182248145]\) \(260549802603/4225\) \(401400694536075\) \([2]\) \(64512\) \(1.9346\)  
7605.q2 7605f1 \([1, -1, 0, -36789, 3036320]\) \(-57960603/8125\) \(-771924412569375\) \([2]\) \(32256\) \(1.5880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7605.q have rank \(0\).

Complex multiplication

The elliptic curves in class 7605.q do not have complex multiplication.

Modular form 7605.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + 4 q^{11} - 2 q^{14} - q^{16} - 4 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.