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Properties

Label 26950i
Number of curves $2$
Conductor $26950$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 26950i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26950.bc1 26950i1 \([1, 0, 1, -1251, -46602]\) \(-117649/440\) \(-808836875000\) \([]\) \(36288\) \(0.97057\) \(\Gamma_0(N)\)-optimal
26950.bc2 26950i2 \([1, 0, 1, 10999, 1104898]\) \(80062991/332750\) \(-611682886718750\) \([]\) \(108864\) \(1.5199\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26950i have rank \(0\).

Complex multiplication

The elliptic curves in class 26950i do not have complex multiplication.

Modular form 26950.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} - 2 q^{9} - q^{11} + q^{12} + 2 q^{13} + q^{16} - 3 q^{17} + 2 q^{18} + q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.