Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.r2 7350s1 \([1, 1, 0, 1200, 1800]\) \(2595575/1512\) \(-111178305000\) \([]\) \(10368\) \(0.80897\) \(\Gamma_0(N)\)-optimal
7350.r1 7350s2 \([1, 1, 0, -17175, 909525]\) \(-7620530425/526848\) \(-38739462720000\) \([]\) \(31104\) \(1.3583\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.s

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