Properties

Label 13200bv
Number of curves $2$
Conductor $13200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 13200bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13200.o1 13200bv1 \([0, -1, 0, -1013, 10572]\) \(57537462272/10673289\) \(21346578000\) \([2]\) \(9216\) \(0.70022\) \(\Gamma_0(N)\)-optimal
13200.o2 13200bv2 \([0, -1, 0, 2012, 58972]\) \(28134667888/64304361\) \(-2057739552000\) \([2]\) \(18432\) \(1.0468\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13200bv have rank \(1\).

Complex multiplication

The elliptic curves in class 13200bv do not have complex multiplication.

Modular form 13200.2.a.bv

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - q^{11} - 4 q^{13} + 8 q^{19} + O(q^{20})\) 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.