Properties

Label 35280.r
Number of curves $3$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.r1 35280ek3 \([0, 0, 0, -926688, 359184112]\) \(-250523582464/13671875\) \(-4802902776000000000\) \([]\) \(622080\) \(2.3429\)  
35280.r2 35280ek1 \([0, 0, 0, -9408, -389648]\) \(-262144/35\) \(-12295431106560\) \([]\) \(69120\) \(1.2443\) \(\Gamma_0(N)\)-optimal
35280.r3 35280ek2 \([0, 0, 0, 61152, 993328]\) \(71991296/42875\) \(-15061903105536000\) \([]\) \(207360\) \(1.7936\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.r have rank \(0\).

Complex multiplication

The elliptic curves in class 35280.r do not have complex multiplication.

Modular form 35280.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3q^{11} - 5q^{13} + 3q^{17} + 2q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.