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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 528.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 528.d1 | 528g3 | \([0, -1, 0, -1288, 18160]\) | \(57736239625/255552\) | \(1046740992\) | \([2]\) | \(288\) | \(0.58307\) | |
| 528.d2 | 528g4 | \([0, -1, 0, -648, 35568]\) | \(-7357983625/127552392\) | \(-522454597632\) | \([2]\) | \(576\) | \(0.92964\) | |
| 528.d3 | 528g1 | \([0, -1, 0, -88, -272]\) | \(18609625/1188\) | \(4866048\) | \([2]\) | \(96\) | \(0.033764\) | \(\Gamma_0(N)\)-optimal |
| 528.d4 | 528g2 | \([0, -1, 0, 72, -1296]\) | \(9938375/176418\) | \(-722608128\) | \([2]\) | \(192\) | \(0.38034\) |
Rank
sage: E.rank()
The elliptic curves in class 528.d have rank \(1\).
Complex multiplication
The elliptic curves in class 528.d do not have complex multiplication.Modular form 528.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
