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Properties

Label 7350.cb
Number of curves $2$
Conductor $7350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cb1 7350bt2 \([1, 1, 1, -5360013, 4774124781]\) \(-14822892630025/42\) \(-48254472656250\) \([]\) \(144000\) \(2.2822\)  
7350.cb2 7350bt1 \([1, 1, 1, 1077, 943641]\) \(46969655/130691232\) \(-384392318839200\) \([]\) \(28800\) \(1.4775\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7350.cb have rank \(1\).

Complex multiplication

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

Modular form 7350.2.a.cb

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.