Properties

Label 3120.v
Number of curves $2$
Conductor $3120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3120.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.v1 3120i2 \([0, 1, 0, -4280, 74100]\) \(4234737878642/1247410125\) \(2554695936000\) \([2]\) \(3840\) \(1.0865\)  
3120.v2 3120i1 \([0, 1, 0, 720, 8100]\) \(40254822716/49359375\) \(-50544000000\) \([2]\) \(1920\) \(0.73996\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3120.v have rank \(1\).

Complex multiplication

The elliptic curves in class 3120.v do not have complex multiplication.

Modular form 3120.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2q^{7} + q^{9} - 4q^{11} - q^{13} + q^{15} - 2q^{19} + O(q^{20})\)  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.