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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 88200.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.m1 | 88200hb4 | \([0, 0, 0, -74091675, 245472151750]\) | \(32779037733124/315\) | \(432261249840000000\) | \([2]\) | \(4718592\) | \(2.9623\) | |
| 88200.m2 | 88200hb6 | \([0, 0, 0, -71445675, -231654568250]\) | \(14695548366242/57421875\) | \(157595247337500000000000\) | \([2]\) | \(9437184\) | \(3.3089\) | |
| 88200.m3 | 88200hb3 | \([0, 0, 0, -6618675, 231610750]\) | \(23366901604/13505625\) | \(18533201086890000000000\) | \([2, 2]\) | \(4718592\) | \(2.9623\) | |
| 88200.m4 | 88200hb2 | \([0, 0, 0, -4634175, 3829509250]\) | \(32082281296/99225\) | \(34040573424900000000\) | \([2, 2]\) | \(2359296\) | \(2.6157\) | |
| 88200.m5 | 88200hb1 | \([0, 0, 0, -169050, 110060125]\) | \(-24918016/229635\) | \(-4923725798958750000\) | \([2]\) | \(1179648\) | \(2.2692\) | \(\Gamma_0(N)\)-optimal |
| 88200.m6 | 88200hb5 | \([0, 0, 0, 26456325, 1852285750]\) | \(746185003198/432360075\) | \(-1186619088256610400000000\) | \([2]\) | \(9437184\) | \(3.3089\) |
Rank
sage: E.rank()
The elliptic curves in class 88200.m have rank \(2\).
Complex multiplication
The elliptic curves in class 88200.m do not have complex multiplication.Modular form 88200.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
