Properties

Label 31200d
Number of curves $4$
Conductor $31200$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.k3 31200d1 \([0, -1, 0, -1658, -23688]\) \(504358336/38025\) \(38025000000\) \([2, 2]\) \(18432\) \(0.77535\) \(\Gamma_0(N)\)-optimal
31200.k4 31200d2 \([0, -1, 0, 1592, -108188]\) \(55742968/658125\) \(-5265000000000\) \([2]\) \(36864\) \(1.1219\)  
31200.k2 31200d3 \([0, -1, 0, -5408, 126312]\) \(2186875592/428415\) \(3427320000000\) \([2]\) \(36864\) \(1.1219\)  
31200.k1 31200d4 \([0, -1, 0, -26033, -1608063]\) \(30488290624/195\) \(12480000000\) \([2]\) \(36864\) \(1.1219\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200d have rank \(0\).

Complex multiplication

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

Modular form 31200.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.