Properties

Label 145656.i
Number of curves $2$
Conductor $145656$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 145656.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145656.i1 145656x2 \([0, 0, 0, -288711, -59692950]\) \(21882096/7\) \(851378788963584\) \([2]\) \(884736\) \(1.8396\)  
145656.i2 145656x1 \([0, 0, 0, -15606, -1193859]\) \(-55296/49\) \(-372478220171568\) \([2]\) \(442368\) \(1.4930\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 145656.i have rank \(1\).

Complex multiplication

The elliptic curves in class 145656.i do not have complex multiplication.

Modular form 145656.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 2 q^{11} + 2 q^{13} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.