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Properties

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

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cw1 7350co2 \([1, 0, 0, -871613, 314735217]\) \(-16591834777/98304\) \(-433881982464000000\) \([]\) \(136080\) \(2.2246\)  
7350.cw2 7350co1 \([1, 0, 0, 28762, 2305092]\) \(596183/864\) \(-3813415861500000\) \([]\) \(45360\) \(1.6753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.cw

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