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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 3360w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3360.y3 | 3360w1 | \([0, 1, 0, -70, 200]\) | \(601211584/11025\) | \(705600\) | \([2, 2]\) | \(768\) | \(-0.082988\) | \(\Gamma_0(N)\)-optimal |
3360.y2 | 3360w2 | \([0, 1, 0, -145, -385]\) | \(82881856/36015\) | \(147517440\) | \([2]\) | \(1536\) | \(0.26359\) | |
3360.y1 | 3360w3 | \([0, 1, 0, -1120, 14060]\) | \(303735479048/105\) | \(53760\) | \([2]\) | \(1536\) | \(0.26359\) | |
3360.y4 | 3360w4 | \([0, 1, 0, 0, 648]\) | \(-8/354375\) | \(-181440000\) | \([4]\) | \(1536\) | \(0.26359\) |
Rank
sage: E.rank()
The elliptic curves in class 3360w have rank \(0\).
Complex multiplication
The elliptic curves in class 3360w do not have complex multiplication.Modular form 3360.2.a.w
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.