↑

Properties

Label 7350.cv
Number of curves $2$
Conductor $7350$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cv1 7350cn1 \([1, 0, 0, -22513, -1304983]\) \(-2637114025/6912\) \(-3307500000000\) \([]\) \(25920\) \(1.2777\) \(\Gamma_0(N)\)-optimal
7350.cv2 7350cn2 \([1, 0, 0, 43112, -6620608]\) \(18519167975/50331648\) \(-24084480000000000\) \([]\) \(77760\) \(1.8270\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7350.cv have rank \(0\).

Complex multiplication

The elliptic curves in class 7350.cv do not have complex multiplication.

Modular form 7350.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + 5 q^{13} + q^{16} - 6 q^{17} + q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.