Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.l1 31200bc4 \([0, -1, 0, -640646033, -6241090296063]\) \(454357982636417669333824/3003024375\) \(192193560000000000\) \([2]\) \(5160960\) \(3.3754\)  
31200.l2 31200bc3 \([0, -1, 0, -42787408, -83359842188]\) \(1082883335268084577352/251301565117746585\) \(2010412520941972680000000\) \([2]\) \(5160960\) \(3.3754\)  
31200.l3 31200bc1 \([0, -1, 0, -40041158, -97503029688]\) \(7099759044484031233216/577161945398025\) \(577161945398025000000\) \([2, 2]\) \(2580480\) \(3.0289\) \(\Gamma_0(N)\)-optimal
31200.l4 31200bc2 \([0, -1, 0, -37307408, -111390479688]\) \(-717825640026599866952/254764560814329735\) \(-2038116486514637880000000\) \([2]\) \(5160960\) \(3.3754\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 31200.2.a.l

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