Properties

Label 433200.m
Number of curves $2$
Conductor $433200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 433200.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433200.m1 433200m2 \([0, -1, 0, -1461448, 680506192]\) \(28662399178/171\) \(2059480486656000\) \([2]\) \(6266880\) \(2.1270\) \(\Gamma_0(N)\)-optimal*
433200.m2 433200m1 \([0, -1, 0, -89648, 11067792]\) \(-13231796/1083\) \(-6521688207744000\) \([2]\) \(3133440\) \(1.7805\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 433200.m1.

Rank

sage: E.rank()
 

The elliptic curves in class 433200.m have rank \(1\).

Complex multiplication

The elliptic curves in class 433200.m do not have complex multiplication.

Modular form 433200.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} + 6 q^{17} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.