Properties

Label 301392.d
Number of curves $2$
Conductor $301392$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 301392.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301392.d1 301392d2 \([0, 0, 0, -1126947, -460456670]\) \(53008645999484449/2060047808\) \(6151269793923072\) \([2]\) \(5750784\) \(2.1142\)  
301392.d2 301392d1 \([0, 0, 0, -67107, -7904990]\) \(-11192824869409/2563305472\) \(-7653989126504448\) \([2]\) \(2875392\) \(1.7676\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301392.d have rank \(0\).

Complex multiplication

The elliptic curves in class 301392.d do not have complex multiplication.

Modular form 301392.2.a.d

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + q^{7} - 4 q^{11} + q^{13} - 8 q^{19} + O(q^{20})\) 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.