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SageMath
E = EllipticCurve("iu1")
E.isogeny_class()
Elliptic curves in class 227850iu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227850.bb4 | 227850iu1 | \([1, 1, 0, -7313275, -20029731875]\) | \(-23531588875176481/80634839040000\) | \(-148228252784640000000000\) | \([2]\) | \(23592960\) | \(3.1322\) | \(\Gamma_0(N)\)-optimal |
| 227850.bb3 | 227850iu2 | \([1, 1, 0, -164113275, -808263331875]\) | \(265917296537844648481/387548045337600\) | \(712416249780051600000000\) | \([2, 2]\) | \(47185920\) | \(3.4788\) | |
| 227850.bb2 | 227850iu3 | \([1, 1, 0, -212133275, -296706271875]\) | \(574303998127522229281/311675678465185440\) | \(572942685871103153602500000\) | \([2]\) | \(94371840\) | \(3.8253\) | |
| 227850.bb1 | 227850iu4 | \([1, 1, 0, -2624893275, -51763634791875]\) | \(1088053867292412065179681/2316066449760\) | \(4257545339809597500000\) | \([2]\) | \(94371840\) | \(3.8253\) |
Rank
sage: E.rank()
The elliptic curves in class 227850iu have rank \(1\).
Complex multiplication
The elliptic curves in class 227850iu do not have complex multiplication.Modular form 227850.2.a.iu
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.
