Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 16245.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.g1 16245b2 \([0, 0, 1, -155838, -23678717]\) \(1590409933520896/45\) \(11842605\) \([]\) \(31104\) \(1.3179\)  
16245.g2 16245b1 \([0, 0, 1, -1938, -31982]\) \(3058794496/91125\) \(23981275125\) \([]\) \(10368\) \(0.76855\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16245.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.