Properties

Label 14616.i
Number of curves $2$
Conductor $14616$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 14616.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14616.i1 14616o2 \([0, 0, 0, -321915, -70298314]\) \(2471097448795250/98942809\) \(147720822294528\) \([2]\) \(73728\) \(1.8018\)  
14616.i2 14616o1 \([0, 0, 0, -19155, -1208482]\) \(-1041220466500/242597383\) \(-181097976019968\) \([2]\) \(36864\) \(1.4552\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14616.i have rank \(1\).

Complex multiplication

The elliptic curves in class 14616.i do not have complex multiplication.

Modular form 14616.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{7} + 4 q^{13} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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 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.