Properties

Label 31200.e
Number of curves $2$
Conductor $31200$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.e1 31200g2 \([0, -1, 0, -830408, -290974188]\) \(7916055336451592/385003125\) \(3080025000000000\) \([2]\) \(276480\) \(2.0444\)  
31200.e2 31200g1 \([0, -1, 0, -49158, -5036688]\) \(-13137573612736/3427734375\) \(-3427734375000000\) \([2]\) \(138240\) \(1.6979\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 31200.e have rank \(0\).

Complex multiplication

The elliptic curves in class 31200.e do not have complex multiplication.

Modular form 31200.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} + q^{13} - 6q^{19} + O(q^{20})\)  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.