Properties

Label 12096.br
Number of curves $3$
Conductor $12096$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 12096.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12096.br1 12096bg3 \([0, 0, 0, -67980, 6822128]\) \(-545407363875/14\) \(-891813888\) \([]\) \(20736\) \(1.2336\)  
12096.br2 12096bg1 \([0, 0, 0, -780, 10736]\) \(-7414875/2744\) \(-19421724672\) \([]\) \(6912\) \(0.68430\) \(\Gamma_0(N)\)-optimal
12096.br3 12096bg2 \([0, 0, 0, 5940, -108432]\) \(4492125/3584\) \(-18492652781568\) \([]\) \(20736\) \(1.2336\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12096.br have rank \(1\).

Complex multiplication

The elliptic curves in class 12096.br do not have complex multiplication.

Modular form 12096.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{7} - 5 q^{13} - 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.