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Properties

Label 388815z
Number of curves $2$
Conductor $388815$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 388815z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388815.z1 388815z1 \([1, 1, 1, -5962370, -4817750218]\) \(1345938541921/203765625\) \(3548838018921818765625\) \([2]\) \(19464192\) \(2.8591\) \(\Gamma_0(N)\)-optimal
388815.z2 388815z2 \([1, 1, 1, 10238255, -26416423468]\) \(6814692748079/21258460125\) \(-370243172838075508180125\) \([2]\) \(38928384\) \(3.2056\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388815z have rank \(0\).

Complex multiplication

The elliptic curves in class 388815z do not have complex multiplication.

Modular form 388815.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3 q^{8} + q^{9} - q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - q^{15} - q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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.