Properties

Label 26520bf
Number of curves $6$
Conductor $26520$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26520bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.bc4 26520bf1 \([0, 1, 0, -16575, 815850]\) \(31476797652269056/49725\) \(795600\) \([4]\) \(22528\) \(0.82665\) \(\Gamma_0(N)\)-optimal
26520.bc3 26520bf2 \([0, 1, 0, -16580, 815328]\) \(1969080716416336/2472575625\) \(632979360000\) \([2, 4]\) \(45056\) \(1.1732\)  
26520.bc5 26520bf3 \([0, 1, 0, -12160, 1264400]\) \(-194204905090564/566398828125\) \(-579992400000000\) \([4]\) \(90112\) \(1.5198\)  
26520.bc2 26520bf4 \([0, 1, 0, -21080, 332928]\) \(1011710313226084/536724738225\) \(549606131942400\) \([2, 2]\) \(90112\) \(1.5198\)  
26520.bc6 26520bf5 \([0, 1, 0, 80320, 2685408]\) \(27980756504588158/17683545112935\) \(-36215900391290880\) \([2]\) \(180224\) \(1.8664\)  
26520.bc1 26520bf6 \([0, 1, 0, -194480, -32821152]\) \(397210600760070242/3536192675535\) \(7242122599495680\) \([2]\) \(180224\) \(1.8664\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26520.2.a.bf

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.