Label 1400.a
Number of curves $2$
Conductor $1400$
CM no
Rank $0$

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
sage: E.isogeny_class()

Elliptic curves in class 1400.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1400.a1 1400h2 [0, 1, 0, -1008, -12512] [2] 640  
1400.a2 1400h1 [0, 1, 0, -8, -512] [2] 320 \(\Gamma_0(N)\)-optimal


sage: E.rank()

The elliptic curves in class 1400.a have rank \(0\).

Complex multiplication

The elliptic curves in class 1400.a do not have complex multiplication.

Modular form 1400.2.a.a

sage: E.q_eigenform(10)
\(q - 2q^{3} - q^{7} + q^{9} + 2q^{17} - 2q^{19} + O(q^{20})\)  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.