Properties

Label 7245s
Number of curves $4$
Conductor $7245$
CM no
Rank $0$
Graph

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

Elliptic curves in class 7245s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7245.s4 7245s1 \([1, -1, 0, -2079, -9072]\) \(1363569097969/734582625\) \(535510733625\) \([2]\) \(8448\) \(0.94164\) \(\Gamma_0(N)\)-optimal
7245.s2 7245s2 \([1, -1, 0, -25884, -1594485]\) \(2630872462131649/3645140625\) \(2657307515625\) \([2, 2]\) \(16896\) \(1.2882\)  
7245.s1 7245s3 \([1, -1, 0, -414009, -102429360]\) \(10765299591712341649/20708625\) \(15096587625\) \([2]\) \(33792\) \(1.6348\)  
7245.s3 7245s4 \([1, -1, 0, -18639, -2511702]\) \(-982374577874929/3183837890625\) \(-2321017822265625\) \([2]\) \(33792\) \(1.6348\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7245s have rank \(0\).

Complex multiplication

The elliptic curves in class 7245s do not have complex multiplication.

Modular form 7245.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} + q^{7} - 3 q^{8} + q^{10} - 4 q^{11} + 2 q^{13} + q^{14} - q^{16} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.