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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 16905.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16905.h1 | 16905z3 | \([1, 0, 0, -247500, -47412513]\) | \(14251520160844849/264449745\) | \(31112248049505\) | \([2]\) | \(92160\) | \(1.7140\) | |
| 16905.h2 | 16905z2 | \([1, 0, 0, -15975, -690768]\) | \(3832302404449/472410225\) | \(55578590561025\) | \([2, 2]\) | \(46080\) | \(1.3674\) | |
| 16905.h3 | 16905z1 | \([1, 0, 0, -3970, 84755]\) | \(58818484369/7455105\) | \(877085648145\) | \([2]\) | \(23040\) | \(1.0208\) | \(\Gamma_0(N)\)-optimal |
| 16905.h4 | 16905z4 | \([1, 0, 0, 23470, -3554475]\) | \(12152722588271/53476250625\) | \(-6291427409780625\) | \([4]\) | \(92160\) | \(1.7140\) |
Rank
sage: E.rank()
The elliptic curves in class 16905.h have rank \(0\).
Complex multiplication
The elliptic curves in class 16905.h do not have complex multiplication.Modular form 16905.2.a.h
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.
