Properties

Label 11310j
Number of curves $6$
Conductor $11310$
CM no
Rank $1$
Graph

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

Elliptic curves in class 11310j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.j4 11310j1 \([1, 1, 1, -10335, 400005]\) \(122083727651299441/32242728960\) \(32242728960\) \([4]\) \(20480\) \(1.0008\) \(\Gamma_0(N)\)-optimal
11310.j3 11310j2 \([1, 1, 1, -11615, 292997]\) \(173294065906331761/61964605497600\) \(61964605497600\) \([2, 4]\) \(40960\) \(1.3474\)  
11310.j2 11310j3 \([1, 1, 1, -78895, -8345755]\) \(54309086480107021681/1575939143610000\) \(1575939143610000\) \([2, 2]\) \(81920\) \(1.6939\)  
11310.j6 11310j4 \([1, 1, 1, 35185, 2108837]\) \(4817210305461175439/4682306425314960\) \(-4682306425314960\) \([4]\) \(81920\) \(1.6939\)  
11310.j1 11310j5 \([1, 1, 1, -1253395, -540629155]\) \(217764763259392950709681/191615146362900\) \(191615146362900\) \([2]\) \(163840\) \(2.0405\)  
11310.j5 11310j6 \([1, 1, 1, 19125, -27596883]\) \(773618103830753999/329643718157812500\) \(-329643718157812500\) \([2]\) \(163840\) \(2.0405\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11310j have rank \(1\).

Complex multiplication

The elliptic curves in class 11310j do not have complex multiplication.

Modular form 11310.2.a.j

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.