Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 400.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400.f1 | 400b4 | \([0, 1, 0, -50208, 4313588]\) | \(-349938025/8\) | \(-320000000000\) | \([]\) | \(720\) | \(1.3211\) | |
| 400.f2 | 400b3 | \([0, 1, 0, -208, 13588]\) | \(-25/2\) | \(-80000000000\) | \([]\) | \(240\) | \(0.77177\) | |
| 400.f3 | 400b1 | \([0, 1, 0, -48, -172]\) | \(-121945/32\) | \(-3276800\) | \([]\) | \(48\) | \(-0.032952\) | \(\Gamma_0(N)\)-optimal |
| 400.f4 | 400b2 | \([0, 1, 0, 352, 1268]\) | \(46969655/32768\) | \(-3355443200\) | \([]\) | \(144\) | \(0.51635\) |
Rank
sage: E.rank()
The elliptic curves in class 400.f have rank \(0\).
Complex multiplication
The elliptic curves in class 400.f do not have complex multiplication.Modular form 400.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
