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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 47190.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47190.i1 | 47190s4 | \([1, 1, 0, -2642036004907, -1652937758403399299]\) | \(1151287518770166280399859009187288721/877598977782384000\) | \(1554720122679137981424000\) | \([2]\) | \(557383680\) | \(5.3340\) | |
| 47190.i2 | 47190s3 | \([1, 1, 0, -166298564907, -25442206797607299]\) | \(287099942490903701230558394328721/8299347173197257908489616000\) | \(14702799777496507417621772610576000\) | \([2]\) | \(557383680\) | \(5.3340\) | |
| 47190.i3 | 47190s2 | \([1, 1, 0, -165127284907, -25827192712503299]\) | \(281076231077501634961715630808721/245403072288481536000000\) | \(434746512146454638397696000000\) | \([2, 2]\) | \(278691840\) | \(4.9875\) | |
| 47190.i4 | 47190s1 | \([1, 1, 0, -10247284907, -409557128503299]\) | \(-67172890180943415009710808721/2029083623424000000000000\) | \(-3594645412996644864000000000000\) | \([2]\) | \(139345920\) | \(4.6409\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.i have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.i do not have complex multiplication.Modular form 47190.2.a.i
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.
