Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 277200.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.o1 | 277200o3 | \([0, 0, 0, -831675, 232578250]\) | \(2727138195938/576489375\) | \(13448344140000000000\) | \([2]\) | \(4718592\) | \(2.3850\) | |
| 277200.o2 | 277200o2 | \([0, 0, 0, -264675, -49220750]\) | \(175798419556/12006225\) | \(140040608400000000\) | \([2, 2]\) | \(2359296\) | \(2.0385\) | |
| 277200.o3 | 277200o1 | \([0, 0, 0, -260175, -51079250]\) | \(667932971344/3465\) | \(10103940000000\) | \([2]\) | \(1179648\) | \(1.6919\) | \(\Gamma_0(N)\)-optimal |
| 277200.o4 | 277200o4 | \([0, 0, 0, 230325, -212075750]\) | \(57925453822/866412855\) | \(-20211679081440000000\) | \([2]\) | \(4718592\) | \(2.3850\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.o have rank \(2\).
Complex multiplication
The elliptic curves in class 277200.o do not have complex multiplication.Modular form 277200.2.a.o
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.
