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SageMath
E = EllipticCurve("il1")
E.isogeny_class()
Elliptic curves in class 316050.il
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
316050.il1 | 316050il4 | \([1, 0, 0, -1027188, -398056758]\) | \(65202655558249/512820150\) | \(942699653552343750\) | \([2]\) | \(5308416\) | \(2.2772\) | |
316050.il2 | 316050il2 | \([1, 0, 0, -108438, 3436992]\) | \(76711450249/41602500\) | \(76476445664062500\) | \([2, 2]\) | \(2654208\) | \(1.9306\) | |
316050.il3 | 316050il1 | \([1, 0, 0, -83938, 9341492]\) | \(35578826569/51600\) | \(94854506250000\) | \([2]\) | \(1327104\) | \(1.5840\) | \(\Gamma_0(N)\)-optimal |
316050.il4 | 316050il3 | \([1, 0, 0, 418312, 27140742]\) | \(4403686064471/2721093750\) | \(-5002093103027343750\) | \([2]\) | \(5308416\) | \(2.2772\) |
Rank
sage: E.rank()
The elliptic curves in class 316050.il have rank \(1\).
Complex multiplication
The elliptic curves in class 316050.il do not have complex multiplication.Modular form 316050.2.a.il
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.