Properties

Label 1872.q
Number of curves $3$
Conductor $1872$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1872.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1872.q1 1872s3 \([0, 0, 0, -66171, -6551638]\) \(-10730978619193/6656\) \(-19874709504\) \([]\) \(4320\) \(1.2968\)  
1872.q2 1872s2 \([0, 0, 0, -651, -12742]\) \(-10218313/17576\) \(-52481654784\) \([]\) \(1440\) \(0.74753\)  
1872.q3 1872s1 \([0, 0, 0, 69, 362]\) \(12167/26\) \(-77635584\) \([]\) \(480\) \(0.19823\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1872.q have rank \(0\).

Complex multiplication

The elliptic curves in class 1872.q do not have complex multiplication.

Modular form 1872.2.a.q

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} + q^{7} + 6 q^{11} + q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.