Properties

Label 380880.u
Number of curves $2$
Conductor $380880$
CM no
Rank $2$
Graph

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

Elliptic curves in class 380880.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380880.u1 380880u2 \([0, 0, 0, -712563, 224043138]\) \(9776035692/359375\) \(1470884593104000000\) \([2]\) \(4866048\) \(2.2554\)  
380880.u2 380880u1 \([0, 0, 0, 17457, 12483342]\) \(574992/66125\) \(-67660691282784000\) \([2]\) \(2433024\) \(1.9088\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 380880.u have rank \(2\).

Complex multiplication

The elliptic curves in class 380880.u do not have complex multiplication.

Modular form 380880.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 2 q^{13} - 6 q^{17} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.