Properties

Label 31200.a
Number of curves $4$
Conductor $31200$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.a1 31200bq4 \([0, -1, 0, -31408, -2131688]\) \(428320044872/73125\) \(585000000000\) \([2]\) \(73728\) \(1.2645\)  
31200.a2 31200bq3 \([0, -1, 0, -13408, 581812]\) \(33324076232/1285245\) \(10281960000000\) \([4]\) \(73728\) \(1.2645\)  
31200.a3 31200bq1 \([0, -1, 0, -2158, -25688]\) \(1111934656/342225\) \(342225000000\) \([2, 2]\) \(36864\) \(0.91789\) \(\Gamma_0(N)\)-optimal
31200.a4 31200bq2 \([0, -1, 0, 5967, -180063]\) \(367061696/426465\) \(-27293760000000\) \([2]\) \(73728\) \(1.2645\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200.a have rank \(1\).

Complex multiplication

The elliptic curves in class 31200.a do not have complex multiplication.

Modular form 31200.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} + 4q^{11} + q^{13} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.