Properties

Label 110400.l
Number of curves $2$
Conductor $110400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 110400.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110400.l1 110400t2 \([0, -1, 0, -85633, 8843137]\) \(33909572018/3234375\) \(6624000000000000\) \([2]\) \(1032192\) \(1.7736\)  
110400.l2 110400t1 \([0, -1, 0, 6367, 655137]\) \(27871484/198375\) \(-203136000000000\) \([2]\) \(516096\) \(1.4270\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 110400.l have rank \(1\).

Complex multiplication

The elliptic curves in class 110400.l do not have complex multiplication.

Modular form 110400.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} + 6 q^{11} - 4 q^{13} - 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.