Properties

Label 3312.j
Number of curves $2$
Conductor $3312$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 3312.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3312.j1 3312d2 \([0, 0, 0, -419835, 104704666]\) \(10963069081334500/1156923\) \(863638391808\) \([2]\) \(14336\) \(1.7186\)  
3312.j2 3312d1 \([0, 0, 0, -26175, 1644478]\) \(-10627137250000/110008287\) \(-20530186553088\) \([2]\) \(7168\) \(1.3721\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3312.j have rank \(1\).

Complex multiplication

The elliptic curves in class 3312.j do not have complex multiplication.

Modular form 3312.2.a.j

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} + 2 q^{13} - 8 q^{17} - 6 q^{19} + O(q^{20})\) 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.