Properties

Label 2535.l
Number of curves $2$
Conductor $2535$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 2535.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2535.l1 2535m2 \([1, 0, 1, -291698, 60610331]\) \(258840217117/18225\) \(193267001072925\) \([2]\) \(14976\) \(1.7940\)  
2535.l2 2535m1 \([1, 0, 1, -17073, 1071631]\) \(-51895117/16875\) \(-178950926919375\) \([2]\) \(7488\) \(1.4474\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2535.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.