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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 4410v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4410.y3 | 4410v1 | \([1, -1, 1, -2288, -36333]\) | \(416832723/56000\) | \(177885288000\) | \([2]\) | \(4608\) | \(0.88616\) | \(\Gamma_0(N)\)-optimal |
| 4410.y4 | 4410v2 | \([1, -1, 1, 3592, -196269]\) | \(1613964717/6125000\) | \(-19456203375000\) | \([2]\) | \(9216\) | \(1.2327\) | |
| 4410.y1 | 4410v3 | \([1, -1, 1, -46388, 3852307]\) | \(4767078987/6860\) | \(15885600931620\) | \([2]\) | \(13824\) | \(1.4355\) | |
| 4410.y2 | 4410v4 | \([1, -1, 1, -33158, 6085531]\) | \(-1740992427/5882450\) | \(-13621902798864150\) | \([2]\) | \(27648\) | \(1.7820\) |
Rank
sage: E.rank()
The elliptic curves in class 4410v have rank \(1\).
Complex multiplication
The elliptic curves in class 4410v do not have complex multiplication.Modular form 4410.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
