Properties

Label 2850.q
Number of curves $4$
Conductor $2850$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2850.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.q1 2850r4 \([1, 1, 1, -186938, -30118969]\) \(46237740924063961/1806561830400\) \(28227528600000000\) \([2]\) \(20736\) \(1.9238\)  
2850.q2 2850r2 \([1, 1, 1, -27563, 1737281]\) \(148212258825961/1218375000\) \(19037109375000\) \([2]\) \(6912\) \(1.3745\)  
2850.q3 2850r1 \([1, 1, 1, -563, 63281]\) \(-1263214441/110808000\) \(-1731375000000\) \([2]\) \(3456\) \(1.0279\) \(\Gamma_0(N)\)-optimal
2850.q4 2850r3 \([1, 1, 1, 5062, -1702969]\) \(918046641959/80912056320\) \(-1264250880000000\) \([2]\) \(10368\) \(1.5772\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2850.q have rank \(1\).

Complex multiplication

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

Modular form 2850.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{12} - 2 q^{13} - 2 q^{14} + q^{16} + q^{18} + q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.