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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 17328.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17328.u1 | 17328bg3 | \([0, 1, 0, -586384, 172633556]\) | \(115714886617/1539\) | \(296565190078464\) | \([4]\) | \(138240\) | \(1.9204\) | |
| 17328.u2 | 17328bg2 | \([0, 1, 0, -37664, 2530356]\) | \(30664297/3249\) | \(626082067943424\) | \([2, 2]\) | \(69120\) | \(1.5738\) | |
| 17328.u3 | 17328bg1 | \([0, 1, 0, -8784, -276780]\) | \(389017/57\) | \(10983895928832\) | \([2]\) | \(34560\) | \(1.2272\) | \(\Gamma_0(N)\)-optimal |
| 17328.u4 | 17328bg4 | \([0, 1, 0, 48976, 12545940]\) | \(67419143/390963\) | \(-75338542175858688\) | \([2]\) | \(138240\) | \(1.9204\) |
Rank
sage: E.rank()
The elliptic curves in class 17328.u have rank \(0\).
Complex multiplication
The elliptic curves in class 17328.u do not have complex multiplication.Modular form 17328.2.a.u
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.
