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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4400.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4400.i1 | 4400m3 | \([0, -1, 0, -3128133, 2130534637]\) | \(-52893159101157376/11\) | \(-704000000\) | \([]\) | \(28000\) | \(1.9946\) | |
| 4400.i2 | 4400m2 | \([0, -1, 0, -4133, 186637]\) | \(-122023936/161051\) | \(-10307264000000\) | \([]\) | \(5600\) | \(1.1899\) | |
| 4400.i3 | 4400m1 | \([0, -1, 0, -133, -1363]\) | \(-4096/11\) | \(-704000000\) | \([]\) | \(1120\) | \(0.38514\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4400.i have rank \(0\).
Complex multiplication
The elliptic curves in class 4400.i do not have complex multiplication.Modular form 4400.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
