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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 141120.dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.dr1 | 141120ds4 | \([0, 0, 0, -847308, -300199088]\) | \(23937672968/45\) | \(126467291381760\) | \([2]\) | \(1179648\) | \(1.9612\) | |
| 141120.dr2 | 141120ds3 | \([0, 0, 0, -141708, 14427952]\) | \(111980168/32805\) | \(92194655417303040\) | \([2]\) | \(1179648\) | \(1.9612\) | |
| 141120.dr3 | 141120ds2 | \([0, 0, 0, -53508, -4587968]\) | \(48228544/2025\) | \(711378514022400\) | \([2, 2]\) | \(589824\) | \(1.6146\) | |
| 141120.dr4 | 141120ds1 | \([0, 0, 0, 1617, -266168]\) | \(85184/5625\) | \(-30875803560000\) | \([2]\) | \(294912\) | \(1.2680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.dr have rank \(2\).
Complex multiplication
The elliptic curves in class 141120.dr do not have complex multiplication.Modular form 141120.2.a.dr
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.
