Properties

Label 331200bc
Number of curves $2$
Conductor $331200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 331200bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
331200.bc2 331200bc1 \([0, 0, 0, 2397300, 719606000]\) \(510273943271/370215360\) \(-1105457141514240000000\) \([2]\) \(12386304\) \(2.7262\) \(\Gamma_0(N)\)-optimal
331200.bc1 331200bc2 \([0, 0, 0, -10850700, 6098294000]\) \(47316161414809/22001657400\) \(65696596969881600000000\) \([2]\) \(24772608\) \(3.0728\)  

Rank

sage: E.rank()
 

The elliptic curves in class 331200bc have rank \(1\).

Complex multiplication

The elliptic curves in class 331200bc do not have complex multiplication.

Modular form 331200.2.a.bc

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - 2 q^{11} + 2 q^{17} + O(q^{20})\) 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.