Properties

Label 100800.lv
Number of curves $4$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("lv1")
 
E.isogeny_class()
 

Elliptic curves in class 100800.lv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.lv1 100800jr4 \([0, 0, 0, -1806300, 934362000]\) \(129348709488/6125\) \(30862944000000000\) \([2]\) \(1327104\) \(2.2379\)  
100800.lv2 100800jr3 \([0, 0, 0, -118800, 12987000]\) \(588791808/109375\) \(34445250000000000\) \([2]\) \(663552\) \(1.8913\)  
100800.lv3 100800jr2 \([0, 0, 0, -42300, -1342000]\) \(1210991472/588245\) \(4065949440000000\) \([2]\) \(442368\) \(1.6886\)  
100800.lv4 100800jr1 \([0, 0, 0, -34800, -2497000]\) \(10788913152/8575\) \(3704400000000\) \([2]\) \(221184\) \(1.3420\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 100800.lv have rank \(1\).

Complex multiplication

The elliptic curves in class 100800.lv do not have complex multiplication.

Modular form 100800.2.a.lv

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