↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.bi1 7350bj1 \([1, 0, 1, -214401, 38192998]\) \(-14822892630025/42\) \(-3088286250\) \([]\) \(28800\) \(1.4775\) \(\Gamma_0(N)\)-optimal
7350.bi2 7350bj2 \([1, 0, 1, 26924, 117901298]\) \(46969655/130691232\) \(-6006129981862500000\) \([]\) \(144000\) \(2.2822\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 2 q^{11} + q^{12} - q^{13} + q^{16} + 3 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.