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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 270480.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.c1 | 270480c6 | \([0, -1, 0, -33229856, -71632346400]\) | \(16841893263968213282/543703603314375\) | \(131002747343529788160000\) | \([2]\) | \(31457280\) | \(3.2098\) | |
| 270480.c2 | 270480c4 | \([0, -1, 0, -5054856, 2817273600]\) | \(118566490663726564/40187675390625\) | \(4841512777760400000000\) | \([2, 2]\) | \(15728640\) | \(2.8632\) | |
| 270480.c3 | 270480c2 | \([0, -1, 0, -4536436, 3719739136]\) | \(342799332162880336/77131175625\) | \(2323047854363040000\) | \([2, 2]\) | \(7864320\) | \(2.5166\) | |
| 270480.c4 | 270480c1 | \([0, -1, 0, -4536191, 3720160830]\) | \(5483900709072173056/277725\) | \(522785096400\) | \([2]\) | \(3932160\) | \(2.1700\) | \(\Gamma_0(N)\)-optimal |
| 270480.c5 | 270480c3 | \([0, -1, 0, -4021936, 4595212336]\) | \(-59722927783102084/41113267272525\) | \(-4953021216097580774400\) | \([2]\) | \(15728640\) | \(2.8632\) | |
| 270480.c6 | 270480c5 | \([0, -1, 0, 14825424, 19500804576]\) | \(1495639267637215678/1547698974609375\) | \(-372910564687500000000000\) | \([2]\) | \(31457280\) | \(3.2098\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.c have rank \(0\).
Complex multiplication
The elliptic curves in class 270480.c do not have complex multiplication.Modular form 270480.2.a.c
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
