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Properties

Label 7350cu
Number of curves $2$
Conductor $7350$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 7350cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cy2 7350cu1 \([1, 0, 0, -2175013, -1225814983]\) \(505318200625/4251528\) \(9573911275753125000\) \([3]\) \(302400\) \(2.4676\) \(\Gamma_0(N)\)-optimal
7350.cy1 7350cu2 \([1, 0, 0, -175818763, -897331751233]\) \(266916252066900625/162\) \(364803813281250\) \([]\) \(907200\) \(3.0169\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.cu

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.