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Properties

Label 123627s
Number of curves $2$
Conductor $123627$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 123627s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123627.l2 123627s1 \([1, 0, 0, -97994, 11783379]\) \(510082399/783\) \(159751104497649\) \([2]\) \(483840\) \(1.6248\) \(\Gamma_0(N)\)-optimal
123627.l1 123627s2 \([1, 0, 0, -127429, 4112618]\) \(1121622319/613089\) \(125085114821659167\) \([2]\) \(967680\) \(1.9714\)  

Rank

sage: E.rank()
 

The elliptic curves in class 123627s have rank \(1\).

Complex multiplication

The elliptic curves in class 123627s do not have complex multiplication.

Modular form 123627.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + q^{9} + 2 q^{10} - q^{12} + 4 q^{13} - 2 q^{15} - q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.