Properties

Label 260100.i
Number of curves $2$
Conductor $260100$
CM \(\Q(\sqrt{-3}) \)
Rank $0$
Graph

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

Elliptic curves in class 260100.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
260100.i1 260100i2 \([0, 0, 0, 0, -5737500]\) \(0\) \(-14220967500000000\) \([]\) \(1516320\) \(1.7783\)   \(-3\)
260100.i2 260100i1 \([0, 0, 0, 0, 212500]\) \(0\) \(-19507500000000\) \([]\) \(505440\) \(1.2290\) \(\Gamma_0(N)\)-optimal \(-3\)

Rank

sage: E.rank()
 

The elliptic curves in class 260100.i have rank \(0\).

Complex multiplication

Each elliptic curve in class 260100.i has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 260100.2.a.i

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