Properties

Label 26520.w
Number of curves $4$
Conductor $26520$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 26520.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.w1 26520z4 \([0, 1, 0, -23576, -1401216]\) \(1415313160121956/89505\) \(91653120\) \([2]\) \(36864\) \(0.98770\)  
26520.w2 26520z3 \([0, 1, 0, -2496, 11280]\) \(1680085884676/910381875\) \(932231040000\) \([2]\) \(36864\) \(0.98770\)  
26520.w3 26520z2 \([0, 1, 0, -1476, -22176]\) \(1390071129424/10989225\) \(2813241600\) \([2, 2]\) \(18432\) \(0.64113\)  
26520.w4 26520z1 \([0, 1, 0, -31, -790]\) \(-212629504/16286595\) \(-260585520\) \([2]\) \(9216\) \(0.29455\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26520.w have rank \(0\).

Complex multiplication

The elliptic curves in class 26520.w do not have complex multiplication.

Modular form 26520.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} - q^{15} - q^{17} + O(q^{20})\) 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 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.