↑

Properties

Label 7245.r
Number of curves $2$
Conductor $7245$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 7245.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7245.r1 7245f1 \([1, -1, 0, -4149, -99232]\) \(292583028222603/8456021875\) \(228312590625\) \([2]\) \(8640\) \(0.95743\) \(\Gamma_0(N)\)-optimal
7245.r2 7245f2 \([1, -1, 0, 996, -332815]\) \(4044759171237/1771943359375\) \(-47842470703125\) \([2]\) \(17280\) \(1.3040\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7245.r have rank \(0\).

Complex multiplication

The elliptic curves in class 7245.r do not have complex multiplication.

Modular form 7245.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - q^{7} - 3 q^{8} + q^{10} + 4 q^{11} + 4 q^{13} - q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.