Properties

Label 2178l
Number of curves $2$
Conductor $2178$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2178l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2178.l2 2178l1 \([1, -1, 1, 3244, 26183]\) \(24167/16\) \(-2500281987984\) \([]\) \(4224\) \(1.0677\) \(\Gamma_0(N)\)-optimal
2178.l1 2178l2 \([1, -1, 1, -56651, 5344859]\) \(-128667913/4096\) \(-640072188923904\) \([3]\) \(12672\) \(1.6170\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2178l have rank \(0\).

Complex multiplication

The elliptic curves in class 2178l do not have complex multiplication.

Modular form 2178.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} + 2 q^{7} + q^{8} + 3 q^{10} + 5 q^{13} + 2 q^{14} + q^{16} - 3 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.