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Properties

Label 216384hl
Number of curves $2$
Conductor $216384$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("hl1")
 
E.isogeny_class()
 

Elliptic curves in class 216384hl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.bb2 216384hl1 \([0, -1, 0, 1111, -5655]\) \(314432/207\) \(-99751292928\) \([2]\) \(184320\) \(0.79931\) \(\Gamma_0(N)\)-optimal
216384.bb1 216384hl2 \([0, -1, 0, -4769, -42111]\) \(3112136/1587\) \(6118079299584\) \([2]\) \(368640\) \(1.1459\)  

Rank

sage: E.rank()
 

The elliptic curves in class 216384hl have rank \(1\).

Complex multiplication

The elliptic curves in class 216384hl do not have complex multiplication.

Modular form 216384.2.a.hl

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} + 2 q^{11} + 6 q^{13} + 2 q^{15} + 4 q^{19} + O(q^{20})\) 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.