Properties

Label 283920im
Number of curves $4$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("im1")
 
E.isogeny_class()
 

Elliptic curves in class 283920im

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.im4 283920im1 \([0, 1, 0, 1644145, -881413272]\) \(6364491337435136/8034291412875\) \(-620479841604604254000\) \([2]\) \(15482880\) \(2.6758\) \(\Gamma_0(N)\)-optimal
283920.im3 283920im2 \([0, 1, 0, -9923060, -8534276100]\) \(87450143958975184/25164018140625\) \(31094248764756996000000\) \([2, 2]\) \(30965760\) \(3.0223\)  
283920.im2 283920im3 \([0, 1, 0, -59355560, 169284312900]\) \(4678944235881273796/202428825314625\) \(1000535322509373216384000\) \([4]\) \(61931520\) \(3.3689\)  
283920.im1 283920im4 \([0, 1, 0, -145565840, -675951010812]\) \(69014771940559650916/9797607421875\) \(48426167994750000000000\) \([2]\) \(61931520\) \(3.3689\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920im have rank \(0\).

Complex multiplication

The elliptic curves in class 283920im do not have complex multiplication.

Modular form 283920.2.a.im

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{7} + q^{9} + 4 q^{11} + q^{15} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.