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Properties

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

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 7350cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cg2 7350cg1 \([1, 1, 1, -44388, 3554781]\) \(505318200625/4251528\) \(81376903125000\) \([]\) \(43200\) \(1.4946\) \(\Gamma_0(N)\)-optimal
7350.cg1 7350cg2 \([1, 1, 1, -3588138, 2614589781]\) \(266916252066900625/162\) \(3100781250\) \([]\) \(129600\) \(2.0439\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 6 q^{11} - q^{12} + 4 q^{13} + q^{16} + 3 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.