Properties

Label 382200u
Number of curves $4$
Conductor $382200$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 382200u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.u3 382200u1 \([0, -1, 0, -557783, 160527312]\) \(652517349376/1365\) \(40147721250000\) \([4]\) \(2949120\) \(1.8593\) \(\Gamma_0(N)\)-optimal
382200.u2 382200u2 \([0, -1, 0, -563908, 156827812]\) \(42140629456/1863225\) \(876826232100000000\) \([2, 2]\) \(5898240\) \(2.2059\)  
382200.u4 382200u3 \([0, -1, 0, 293592, 590722812]\) \(1486779836/80970435\) \(-152417451317040000000\) \([2]\) \(11796480\) \(2.5524\)  
382200.u1 382200u4 \([0, -1, 0, -1519408, -513933188]\) \(206081497444/58524375\) \(110165347110000000000\) \([2]\) \(11796480\) \(2.5524\)  

Rank

sage: E.rank()
 

The elliptic curves in class 382200u have rank \(2\).

Complex multiplication

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

Modular form 382200.2.a.u

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