Properties

Label 481338u
Number of curves $2$
Conductor $481338$
CM no
Rank $0$
Graph

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

Elliptic curves in class 481338u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.u1 481338u1 \([1, -1, 0, -20811357, -35316029435]\) \(771864882375147625/29358565696512\) \(37915647212827423024128\) \([2]\) \(32768000\) \(3.1006\) \(\Gamma_0(N)\)-optimal
481338.u2 481338u2 \([1, -1, 0, 8635203, -127265857691]\) \(55138849409108375/5449537181735712\) \(-7037902716086203871408928\) \([2]\) \(65536000\) \(3.4472\)  

Rank

sage: E.rank()
 

The elliptic curves in class 481338u have rank \(0\).

Complex multiplication

The elliptic curves in class 481338u do not have complex multiplication.

Modular form 481338.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} + q^{13} + 2 q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.