Properties

Label 273325l
Number of curves $2$
Conductor $273325$
CM no
Rank $1$
Graph

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

Elliptic curves in class 273325l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273325.l2 273325l1 \([0, 1, 1, -2803, 52134]\) \(163840/13\) \(193317579325\) \([]\) \(299376\) \(0.90922\) \(\Gamma_0(N)\)-optimal
273325.l1 273325l2 \([0, 1, 1, -44853, -3660881]\) \(671088640/2197\) \(32670670905925\) \([]\) \(898128\) \(1.4585\)  

Rank

sage: E.rank()
 

The elliptic curves in class 273325l have rank \(1\).

Complex multiplication

The elliptic curves in class 273325l do not have complex multiplication.

Modular form 273325.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + 4 q^{7} - 2 q^{9} + 6 q^{11} - 2 q^{12} - q^{13} + 4 q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.