Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 361920h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.h2 | 361920h1 | \([0, -1, 0, -1096836, 442559286]\) | \(-2280180477309525902656/314018173828125\) | \(-20097163125000000\) | \([2]\) | \(6717440\) | \(2.1459\) | \(\Gamma_0(N)\)-optimal |
| 361920.h1 | 361920h2 | \([0, -1, 0, -17549961, 28304281161]\) | \(145946019963295373639104/2767415625\) | \(11335334400000\) | \([2]\) | \(13434880\) | \(2.4925\) |
Rank
sage: E.rank()
The elliptic curves in class 361920h have rank \(1\).
Complex multiplication
The elliptic curves in class 361920h do not have complex multiplication.Modular form 361920.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
