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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 152880gm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.fb4 | 152880gm1 | \([0, 1, 0, -112471, -12277420]\) | \(83587439220736/13990184325\) | \(26334899130430800\) | \([2]\) | \(884736\) | \(1.8719\) | \(\Gamma_0(N)\)-optimal |
| 152880.fb2 | 152880gm2 | \([0, 1, 0, -1719916, -868724116]\) | \(18681746265374416/693005625\) | \(20872043206560000\) | \([2, 2]\) | \(1769472\) | \(2.2185\) | |
| 152880.fb3 | 152880gm3 | \([0, 1, 0, -1640536, -952454140]\) | \(-4053153720264484/903687890625\) | \(-108869608083600000000\) | \([2]\) | \(3538944\) | \(2.5651\) | |
| 152880.fb1 | 152880gm4 | \([0, 1, 0, -27518416, -55571863516]\) | \(19129597231400697604/26325\) | \(3171440563200\) | \([2]\) | \(3538944\) | \(2.5651\) |
Rank
sage: E.rank()
The elliptic curves in class 152880gm have rank \(1\).
Complex multiplication
The elliptic curves in class 152880gm do not have complex multiplication.Modular form 152880.2.a.gm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
