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Properties

Label 16245.l
Number of curves $2$
Conductor $16245$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 16245.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.l1 16245f2 \([1, -1, 0, -271359, 43167438]\) \(9393931/2025\) \(476359646653804275\) \([2]\) \(194560\) \(2.1061\)  
16245.l2 16245f1 \([1, -1, 0, 37296, 4091715]\) \(24389/45\) \(-10585769925640095\) \([2]\) \(97280\) \(1.7596\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16245.l have rank \(1\).

Complex multiplication

The elliptic curves in class 16245.l do not have complex multiplication.

Modular form 16245.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} + 2 q^{7} - 3 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} + 2 q^{14} - q^{16} - 6 q^{17} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.