Properties

Label 41400.ba
Number of curves $4$
Conductor $41400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 41400.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41400.ba1 41400bm4 \([0, 0, 0, -237675, -43888250]\) \(63649751618/1164375\) \(27162540000000000\) \([2]\) \(294912\) \(1.9483\)  
41400.ba2 41400bm2 \([0, 0, 0, -30675, 1030750]\) \(273671716/119025\) \(1388307600000000\) \([2, 2]\) \(147456\) \(1.6017\)  
41400.ba3 41400bm1 \([0, 0, 0, -26175, 1629250]\) \(680136784/345\) \(1006020000000\) \([4]\) \(73728\) \(1.2551\) \(\Gamma_0(N)\)-optimal
41400.ba4 41400bm3 \([0, 0, 0, 104325, 7645750]\) \(5382838942/4197615\) \(-97921962720000000\) \([2]\) \(294912\) \(1.9483\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41400.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 41400.ba do not have complex multiplication.

Modular form 41400.2.a.ba

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} - 2 q^{13} + 2 q^{17} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.