Properties

Label 26520c
Number of curves $4$
Conductor $26520$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26520c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.v3 26520c1 \([0, 1, 0, -476, 3264]\) \(46689225424/7249905\) \(1855975680\) \([2]\) \(12288\) \(0.50172\) \(\Gamma_0(N)\)-optimal
26520.v2 26520c2 \([0, 1, 0, -2096, -34320]\) \(994958062276/98903025\) \(101276697600\) \([2, 2]\) \(24576\) \(0.84829\)  
26520.v4 26520c3 \([0, 1, 0, 2584, -161616]\) \(931329171502/6107473125\) \(-12508104960000\) \([2]\) \(49152\) \(1.1949\)  
26520.v1 26520c4 \([0, 1, 0, -32696, -2286480]\) \(1887517194957938/21849165\) \(44747089920\) \([2]\) \(49152\) \(1.1949\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26520c have rank \(1\).

Complex multiplication

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

Modular form 26520.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.