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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4400.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4400.x1 | 4400j2 | \([0, -1, 0, -5708, 104912]\) | \(41141648/14641\) | \(7320500000000\) | \([2]\) | \(7680\) | \(1.1695\) | |
| 4400.x2 | 4400j1 | \([0, -1, 0, -5083, 141162]\) | \(464857088/121\) | \(3781250000\) | \([2]\) | \(3840\) | \(0.82291\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4400.x have rank \(1\).
Complex multiplication
The elliptic curves in class 4400.x do not have complex multiplication.Modular form 4400.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
