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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3360.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3360.a1 | 3360d2 | \([0, -1, 0, -376, -2684]\) | \(11512557512/2835\) | \(1451520\) | \([2]\) | \(1024\) | \(0.17027\) | |
3360.a2 | 3360d3 | \([0, -1, 0, -176, 936]\) | \(1184287112/36015\) | \(18439680\) | \([2]\) | \(1024\) | \(0.17027\) | |
3360.a3 | 3360d1 | \([0, -1, 0, -26, -24]\) | \(31554496/11025\) | \(705600\) | \([2, 2]\) | \(512\) | \(-0.17631\) | \(\Gamma_0(N)\)-optimal |
3360.a4 | 3360d4 | \([0, -1, 0, 79, -255]\) | \(13144256/13125\) | \(-53760000\) | \([2]\) | \(1024\) | \(0.17027\) |
Rank
sage: E.rank()
The elliptic curves in class 3360.a have rank \(1\).
Complex multiplication
The elliptic curves in class 3360.a do not have complex multiplication.Modular form 3360.2.a.a
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.