Properties

Label 400.c
Number of curves $4$
Conductor $400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 400.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400.c1 400e3 \([0, 1, 0, -1033, 12438]\) \(488095744/125\) \(31250000\) \([2]\) \(144\) \(0.42408\)  
400.c2 400e4 \([0, 1, 0, -908, 15688]\) \(-20720464/15625\) \(-62500000000\) \([2]\) \(288\) \(0.77065\)  
400.c3 400e1 \([0, 1, 0, -33, -62]\) \(16384/5\) \(1250000\) \([2]\) \(48\) \(-0.12523\) \(\Gamma_0(N)\)-optimal
400.c4 400e2 \([0, 1, 0, 92, -312]\) \(21296/25\) \(-100000000\) \([2]\) \(96\) \(0.22134\)  

Rank

sage: E.rank()
 

The elliptic curves in class 400.c have rank \(0\).

Complex multiplication

The elliptic curves in class 400.c do not have complex multiplication.

Modular form 400.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + 2q^{7} + q^{9} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.