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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 203280.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.dd1 | 203280ci3 | \([0, -1, 0, -1113233920, 14296806174400]\) | \(21026497979043461623321/161783881875\) | \(1173954623727029760000\) | \([4]\) | \(58982400\) | \(3.6354\) | |
| 203280.dd2 | 203280ci2 | \([0, -1, 0, -69623440, 223092685312]\) | \(5143681768032498601/14238434358225\) | \(103318548521334535065600\) | \([2, 2]\) | \(29491200\) | \(3.2888\) | |
| 203280.dd3 | 203280ci4 | \([0, -1, 0, -42180640, 400724441152]\) | \(-1143792273008057401/8897444448004035\) | \(-64562649431041950714408960\) | \([2]\) | \(58982400\) | \(3.6354\) | |
| 203280.dd4 | 203280ci1 | \([0, -1, 0, -6112960, 399538240]\) | \(3481467828171481/2005331497785\) | \(14551314733250528808960\) | \([2]\) | \(14745600\) | \(2.9422\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.dd have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.dd do not have complex multiplication.Modular form 203280.2.a.dd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
