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SageMath
E = EllipticCurve("lp1")
E.isogeny_class()
Elliptic curves in class 158400lp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.is3 | 158400lp1 | \([0, 0, 0, -11100, 434000]\) | \(810448/33\) | \(6158592000000\) | \([2]\) | \(262144\) | \(1.2199\) | \(\Gamma_0(N)\)-optimal |
| 158400.is2 | 158400lp2 | \([0, 0, 0, -29100, -1330000]\) | \(3650692/1089\) | \(812934144000000\) | \([2, 2]\) | \(524288\) | \(1.5664\) | |
| 158400.is4 | 158400lp3 | \([0, 0, 0, 78900, -8890000]\) | \(36382894/43923\) | \(-65576687616000000\) | \([2]\) | \(1048576\) | \(1.9130\) | |
| 158400.is1 | 158400lp4 | \([0, 0, 0, -425100, -106666000]\) | \(5690357426/891\) | \(1330255872000000\) | \([2]\) | \(1048576\) | \(1.9130\) |
Rank
sage: E.rank()
The elliptic curves in class 158400lp have rank \(1\).
Complex multiplication
The elliptic curves in class 158400lp do not have complex multiplication.Modular form 158400.2.a.lp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
