Properties

Label 50400df
Number of curves $4$
Conductor $50400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 50400df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50400.ca3 50400df1 \([0, 0, 0, -1435218825, -20927879219000]\) \(448487713888272974160064/91549016015625\) \(66739232675390625000000\) \([2, 2]\) \(20643840\) \(3.7674\) \(\Gamma_0(N)\)-optimal
50400.ca4 50400df2 \([0, 0, 0, -1430298075, -21078508297250]\) \(-55486311952875723077768/801237030029296875\) \(-4672814359130859375000000000\) \([2]\) \(41287680\) \(4.1140\)  
50400.ca2 50400df3 \([0, 0, 0, -1440140700, -20777112344000]\) \(7079962908642659949376/100085966990454375\) \(4669610875906639320000000000\) \([2]\) \(41287680\) \(4.1140\)  
50400.ca1 50400df4 \([0, 0, 0, -22963500075, -1339384407812750]\) \(229625675762164624948320008/9568125\) \(55801305000000000\) \([2]\) \(41287680\) \(4.1140\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50400df have rank \(1\).

Complex multiplication

The elliptic curves in class 50400df do not have complex multiplication.

Modular form 50400.2.a.df

sage: E.q_eigenform(10)
 
\(q - q^{7} + 4q^{11} + 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.