Properties

Label 270400.ig
Number of curves $2$
Conductor $270400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ig1")
 
E.isogeny_class()
 

Elliptic curves in class 270400.ig

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270400.ig1 270400ig2 \([0, -1, 0, -122550913, 522224116257]\) \(-6434774386429585/140608\) \(-4447849413817139200\) \([]\) \(34836480\) \(3.1046\)  
270400.ig2 270400ig1 \([0, -1, 0, -1411713, 816771617]\) \(-9836106385/3407872\) \(-107801131355000012800\) \([]\) \(11612160\) \(2.5553\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 270400.ig have rank \(0\).

Complex multiplication

The elliptic curves in class 270400.ig do not have complex multiplication.

Modular form 270400.2.a.ig

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 5 q^{7} + q^{9} + 3 q^{11} - 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.