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Properties

Label 1350.d
Number of curves $2$
Conductor $1350$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1350.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1350.d1 1350g2 \([1, -1, 0, -35817, -2600659]\) \(-16522921323/4000\) \(-1230187500000\) \([]\) \(4320\) \(1.3087\)  
1350.d2 1350g1 \([1, -1, 0, 183, -12659]\) \(1601613/163840\) \(-69120000000\) \([]\) \(1440\) \(0.75935\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1350.d have rank \(0\).

Complex multiplication

The elliptic curves in class 1350.d do not have complex multiplication.

Modular form 1350.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} + 3 q^{11} - 5 q^{13} + 2 q^{14} + q^{16} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.