Properties

Label 7605.r
Number of curves $2$
Conductor $7605$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7605.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7605.r1 7605g2 \([1, -1, 0, -31719, 2084850]\) \(12326391/625\) \(178950926919375\) \([2]\) \(29952\) \(1.4931\)  
7605.r2 7605g1 \([1, -1, 0, 1236, 127323]\) \(729/25\) \(-7158037076775\) \([2]\) \(14976\) \(1.1466\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7605.r have rank \(1\).

Complex multiplication

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

Modular form 7605.2.a.r

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