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Properties

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

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.bl1 7350u2 \([1, 0, 1, -172751, -28687102]\) \(-6329617441/279936\) \(-25215239574000000\) \([]\) \(82320\) \(1.9122\)  
7350.bl2 7350u1 \([1, 0, 1, -1251, 39148]\) \(-2401/6\) \(-540450093750\) \([]\) \(11760\) \(0.93920\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 5 q^{11} + q^{12} + q^{16} + 4 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.