Properties

Label 7935.j
Number of curves $4$
Conductor $7935$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 7935.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7935.j1 7935j3 \([1, 0, 1, -15940633, -24488418157]\) \(3026030815665395929/1364501953125\) \(201995259673095703125\) \([2]\) \(633600\) \(2.8540\)  
7935.j2 7935j4 \([1, 0, 1, -8762103, 9808700131]\) \(502552788401502649/10024505152875\) \(1483986532090931530875\) \([4]\) \(633600\) \(2.8540\)  
7935.j3 7935j2 \([1, 0, 1, -1157728, -250367119]\) \(1159246431432649/488076890625\) \(72252896404027640625\) \([2, 2]\) \(316800\) \(2.5074\)  
7935.j4 7935j1 \([1, 0, 1, 241477, -28733047]\) \(10519294081031/8500170375\) \(-1258330278114588375\) \([2]\) \(158400\) \(2.1609\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7935.j have rank \(0\).

Complex multiplication

The elliptic curves in class 7935.j do not have complex multiplication.

Modular form 7935.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 4 q^{7} - 3 q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{15} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.