Properties

Label 382200el
Number of curves $4$
Conductor $382200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("el1")
 
E.isogeny_class()
 

Elliptic curves in class 382200el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.el4 382200el1 \([0, -1, 0, 53492, 56809012]\) \(35969456/2985255\) \(-1404849061980000000\) \([2]\) \(5898240\) \(2.1617\) \(\Gamma_0(N)\)-optimal
382200.el3 382200el2 \([0, -1, 0, -1931008, 997462012]\) \(423026849956/16769025\) \(31565744355600000000\) \([2, 2]\) \(11796480\) \(2.5083\)  
382200.el1 382200el3 \([0, -1, 0, -30596008, 65149732012]\) \(841356017734178/1404585\) \(5287936661280000000\) \([2]\) \(23592960\) \(2.8548\)  
382200.el2 382200el4 \([0, -1, 0, -5018008, -2984767988]\) \(3711757787138/1124589375\) \(4233818092140000000000\) \([2]\) \(23592960\) \(2.8548\)  

Rank

sage: E.rank()
 

The elliptic curves in class 382200el have rank \(0\).

Complex multiplication

The elliptic curves in class 382200el do not have complex multiplication.

Modular form 382200.2.a.el

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 4 q^{11} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.