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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4400g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.c2 | 4400g1 | \([0, 1, 0, 12, 28]\) | \(5488/11\) | \(-352000\) | \([2]\) | \(640\) | \(-0.25126\) | \(\Gamma_0(N)\)-optimal |
4400.c1 | 4400g2 | \([0, 1, 0, -88, 228]\) | \(595508/121\) | \(15488000\) | \([2]\) | \(1280\) | \(0.095312\) |
Rank
sage: E.rank()
The elliptic curves in class 4400g have rank \(2\).
Complex multiplication
The elliptic curves in class 4400g do not have complex multiplication.Modular form 4400.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.