Properties

Label 91200.l
Number of curves $2$
Conductor $91200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 91200.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91200.l1 91200ci2 \([0, -1, 0, -404833, 99277537]\) \(28662399178/171\) \(43776000000000\) \([2]\) \(696320\) \(1.8061\)  
91200.l2 91200ci1 \([0, -1, 0, -24833, 1617537]\) \(-13231796/1083\) \(-138624000000000\) \([2]\) \(348160\) \(1.4595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 91200.l have rank \(1\).

Complex multiplication

The elliptic curves in class 91200.l do not have complex multiplication.

Modular form 91200.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.