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Properties

Label 7350.bv
Number of curves $2$
Conductor $7350$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.bv1 7350bo1 \([1, 1, 1, -1103138, 446506031]\) \(-2637114025/6912\) \(-389124067500000000\) \([]\) \(181440\) \(2.2506\) \(\Gamma_0(N)\)-optimal
7350.bv2 7350bo2 \([1, 1, 1, 2112487, 2272981031]\) \(18519167975/50331648\) \(-2833514987520000000000\) \([]\) \(544320\) \(2.7999\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.bv

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.