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Properties

Label 2535.k
Number of curves $8$
Conductor $2535$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 2535.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2535.k1 2535f7 \([1, 0, 1, -21970004, -39638148769]\) \(242970740812818720001/24375\) \(117653469375\) \([2]\) \(64512\) \(2.4719\)  
2535.k2 2535f5 \([1, 0, 1, -1373129, -619428769]\) \(59319456301170001/594140625\) \(2867803316015625\) \([2, 2]\) \(32256\) \(2.1253\)  
2535.k3 2535f8 \([1, 0, 1, -1340174, -650564653]\) \(-55150149867714721/5950927734375\) \(-28723991546630859375\) \([2]\) \(64512\) \(2.4719\)  
2535.k4 2535f3 \([1, 0, 1, -87884, -9194443]\) \(15551989015681/1445900625\) \(6979086149855625\) \([2, 2]\) \(16128\) \(1.7787\)  
2535.k5 2535f2 \([1, 0, 1, -19439, 880661]\) \(168288035761/27720225\) \(133800231512025\) \([2, 2]\) \(8064\) \(1.4322\)  
2535.k6 2535f1 \([1, 0, 1, -18594, 974287]\) \(147281603041/5265\) \(25413149385\) \([2]\) \(4032\) \(1.0856\) \(\Gamma_0(N)\)-optimal
2535.k7 2535f4 \([1, 0, 1, 35486, 4967081]\) \(1023887723039/2798036865\) \(-13505589522313785\) \([2]\) \(16128\) \(1.7787\)  
2535.k8 2535f6 \([1, 0, 1, 102241, -43492993]\) \(24487529386319/183539412225\) \(-885909686782340025\) \([2]\) \(32256\) \(2.1253\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2535.k have rank \(0\).

Complex multiplication

The elliptic curves in class 2535.k do not have complex multiplication.

Modular form 2535.2.a.k

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.