Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cf1 7350bx1 \([1, 1, 1, -1308938, 328171031]\) \(393349474783/153600000\) \(96848656800000000000\) \([2]\) \(376320\) \(2.5337\) \(\Gamma_0(N)\)-optimal
7350.cf2 7350bx2 \([1, 1, 1, 4179062, 2369707031]\) \(12801408679457/11250000000\) \(-7093407480468750000000\) \([2]\) \(752640\) \(2.8803\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.cf

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.