Properties

Label 327990bc
Number of curves $2$
Conductor $327990$
CM no
Rank $1$
Graph

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

Elliptic curves in class 327990bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bc1 327990bc1 \([1, 1, 1, -700150, 191543027]\) \(63812982460681/10201800960\) \(6068269127208188160\) \([2]\) \(6451200\) \(2.3265\) \(\Gamma_0(N)\)-optimal
327990.bc2 327990bc2 \([1, 1, 1, 1250970, 1070327475]\) \(363979050334199/1041836936400\) \(-619708906449913784400\) \([2]\) \(12902400\) \(2.6731\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990bc have rank \(1\).

Complex multiplication

The elliptic curves in class 327990bc do not have complex multiplication.

Modular form 327990.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} - q^{13} - q^{15} + q^{16} + 4 q^{17} + q^{18} + O(q^{20})\)  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.