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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 381150db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.db3 | 381150db1 | \([1, -1, 0, -13640292, -16833360384]\) | \(13908844989649/1980372240\) | \(39962301791512196250000\) | \([2]\) | \(35389440\) | \(3.0626\) | \(\Gamma_0(N)\)-optimal |
| 381150.db2 | 381150db2 | \([1, -1, 0, -57744792, 152130979116]\) | \(1055257664218129/115307784900\) | \(2326817355854560439062500\) | \([2, 2]\) | \(70778880\) | \(3.4092\) | |
| 381150.db1 | 381150db3 | \([1, -1, 0, -898180542, 10360904034366]\) | \(3971101377248209009/56495958750\) | \(1140042517243285605468750\) | \([2]\) | \(141557760\) | \(3.7558\) | |
| 381150.db4 | 381150db4 | \([1, -1, 0, 77018958, 756546397866]\) | \(2503876820718671/13702874328990\) | \(-276512863736296142520468750\) | \([2]\) | \(141557760\) | \(3.7558\) |
Rank
sage: E.rank()
The elliptic curves in class 381150db have rank \(1\).
Complex multiplication
The elliptic curves in class 381150db do not have complex multiplication.Modular form 381150.2.a.db
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.
