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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 4400.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4400.k1 | 4400w3 | \([0, -1, 0, -12131208, -16259299088]\) | \(-24680042791780949/369098752\) | \(-2952790016000000000\) | \([]\) | \(144000\) | \(2.6810\) | |
| 4400.k2 | 4400w1 | \([0, -1, 0, -11208, 460912]\) | \(-19465109/22\) | \(-176000000000\) | \([]\) | \(5760\) | \(1.0716\) | \(\Gamma_0(N)\)-optimal |
| 4400.k3 | 4400w2 | \([0, -1, 0, 78792, -4819088]\) | \(6761990971/5153632\) | \(-41229056000000000\) | \([]\) | \(28800\) | \(1.8763\) |
Rank
sage: E.rank()
The elliptic curves in class 4400.k have rank \(1\).
Complex multiplication
The elliptic curves in class 4400.k do not have complex multiplication.Modular form 4400.2.a.k
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.
\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
