Properties

Label 302016bj
Number of curves $2$
Conductor $302016$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 302016bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
302016.bj1 302016bj1 \([0, -1, 0, -1613, -10899]\) \(256000/117\) \(212247180288\) \([2]\) \(358400\) \(0.86835\) \(\Gamma_0(N)\)-optimal
302016.bj2 302016bj2 \([0, -1, 0, 5647, -87855]\) \(686000/507\) \(-14715804499968\) \([2]\) \(716800\) \(1.2149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 302016bj have rank \(1\).

Complex multiplication

The elliptic curves in class 302016bj do not have complex multiplication.

Modular form 302016.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.