↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 7605j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7605.f1 7605j1 \([1, -1, 1, -1553, -4624]\) \(117649/65\) \(228718344465\) \([2]\) \(8064\) \(0.87017\) \(\Gamma_0(N)\)-optimal
7605.f2 7605j2 \([1, -1, 1, 6052, -41128]\) \(6967871/4225\) \(-14866692390225\) \([2]\) \(16128\) \(1.2167\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7605.2.a.j

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