Properties

Label 2850i
Number of curves $4$
Conductor $2850$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2850i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.m3 2850i1 \([1, 0, 1, -776, 8198]\) \(3301293169/22800\) \(356250000\) \([2]\) \(1536\) \(0.47449\) \(\Gamma_0(N)\)-optimal
2850.m2 2850i2 \([1, 0, 1, -1276, -3802]\) \(14688124849/8122500\) \(126914062500\) \([2, 2]\) \(3072\) \(0.82106\)  
2850.m1 2850i3 \([1, 0, 1, -15526, -744802]\) \(26487576322129/44531250\) \(695800781250\) \([2]\) \(6144\) \(1.1676\)  
2850.m4 2850i4 \([1, 0, 1, 4974, -28802]\) \(871257511151/527800050\) \(-8246875781250\) \([2]\) \(6144\) \(1.1676\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2850i have rank \(0\).

Complex multiplication

The elliptic curves in class 2850i do not have complex multiplication.

Modular form 2850.2.a.i

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