Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 400.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400.d1 | 400c2 | \([0, -1, 0, -2008, 35312]\) | \(-349938025/8\) | \(-20480000\) | \([]\) | \(144\) | \(0.51635\) | |
| 400.d2 | 400c3 | \([0, -1, 0, -1208, -19088]\) | \(-121945/32\) | \(-51200000000\) | \([]\) | \(240\) | \(0.77177\) | |
| 400.d3 | 400c1 | \([0, -1, 0, -8, 112]\) | \(-25/2\) | \(-5120000\) | \([]\) | \(48\) | \(-0.032952\) | \(\Gamma_0(N)\)-optimal |
| 400.d4 | 400c4 | \([0, -1, 0, 8792, 140912]\) | \(46969655/32768\) | \(-52428800000000\) | \([]\) | \(720\) | \(1.3211\) |
Rank
sage: E.rank()
The elliptic curves in class 400.d have rank \(1\).
Complex multiplication
The elliptic curves in class 400.d do not have complex multiplication.Modular form 400.2.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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
