Properties

Label 388080jr
Number of curves $2$
Conductor $388080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jr1")
 
E.isogeny_class()
 

Elliptic curves in class 388080jr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.jr1 388080jr1 \([0, 0, 0, -53067, -4629814]\) \(188183524/3465\) \(304311919887360\) \([2]\) \(1769472\) \(1.5737\) \(\Gamma_0(N)\)-optimal
388080.jr2 388080jr2 \([0, 0, 0, -147, -13446286]\) \(-2/444675\) \(-78106726104422400\) \([2]\) \(3538944\) \(1.9203\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080jr have rank \(0\).

Complex multiplication

The elliptic curves in class 388080jr do not have complex multiplication.

Modular form 388080.2.a.jr

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{11} + 8 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.