Properties

Label 212940bj
Number of curves $2$
Conductor $212940$
CM no
Rank $0$
Graph

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

Elliptic curves in class 212940bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212940.m2 212940bj1 \([0, 0, 0, 312, 6253]\) \(131072/735\) \(-18834968880\) \([2]\) \(119808\) \(0.65360\) \(\Gamma_0(N)\)-optimal
212940.m1 212940bj2 \([0, 0, 0, -3783, 80782]\) \(14602768/1575\) \(645770361600\) \([2]\) \(239616\) \(1.0002\)  

Rank

sage: E.rank()
 

The elliptic curves in class 212940bj have rank \(0\).

Complex multiplication

The elliptic curves in class 212940bj do not have complex multiplication.

Modular form 212940.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + 4 q^{11} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.