Properties

Label 388080em
Number of curves $2$
Conductor $388080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("em1")
 
E.isogeny_class()
 

Elliptic curves in class 388080em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.em2 388080em1 \([0, 0, 0, -4368, 92428]\) \(1007878144/179685\) \(1643143138560\) \([]\) \(497664\) \(1.0633\) \(\Gamma_0(N)\)-optimal
388080.em1 388080em2 \([0, 0, 0, -337008, 75302332]\) \(462893166690304/4125\) \(37721376000\) \([]\) \(1492992\) \(1.6126\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080em have rank \(1\).

Complex multiplication

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

Modular form 388080.2.a.em

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{11} - 5 q^{13} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.