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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 110946.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110946.w1 | 110946t4 | \([1, 1, 1, -42662134, -107270711965]\) | \(1807791328511035057/13428016272\) | \(63784477041844209552\) | \([2]\) | \(10321920\) | \(2.9763\) | |
| 110946.w2 | 110946t2 | \([1, 1, 1, -2721574, -1603966429]\) | \(469332926706097/37959508224\) | \(180311621001096777984\) | \([2, 2]\) | \(5160960\) | \(2.6297\) | |
| 110946.w3 | 110946t1 | \([1, 1, 1, -569894, 136312355]\) | \(4309261738417/798031872\) | \(3790734579640369152\) | \([4]\) | \(2580480\) | \(2.2832\) | \(\Gamma_0(N)\)-optimal |
| 110946.w4 | 110946t3 | \([1, 1, 1, 2792106, -7272029469]\) | \(506776266613583/5104222958736\) | \(-24245591123301441599376\) | \([2]\) | \(10321920\) | \(2.9763\) |
Rank
sage: E.rank()
The elliptic curves in class 110946.w have rank \(0\).
Complex multiplication
The elliptic curves in class 110946.w do not have complex multiplication.Modular form 110946.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
