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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5880.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5880.z1 | 5880bc5 | \([0, 1, 0, -1195616, 502673184]\) | \(784478485879202/221484375\) | \(53365586400000000\) | \([2]\) | \(98304\) | \(2.1907\) | |
| 5880.z2 | 5880bc3 | \([0, 1, 0, -84296, 5690880]\) | \(549871953124/200930625\) | \(24206629991040000\) | \([2, 2]\) | \(49152\) | \(1.8441\) | |
| 5880.z3 | 5880bc2 | \([0, 1, 0, -36276, -2606976]\) | \(175293437776/4862025\) | \(146435169081600\) | \([2, 2]\) | \(24576\) | \(1.4976\) | |
| 5880.z4 | 5880bc1 | \([0, 1, 0, -36031, -2644510]\) | \(2748251600896/2205\) | \(4150656720\) | \([2]\) | \(12288\) | \(1.1510\) | \(\Gamma_0(N)\)-optimal |
| 5880.z5 | 5880bc4 | \([0, 1, 0, 7824, -8498736]\) | \(439608956/259416045\) | \(-31252519196881920\) | \([2]\) | \(49152\) | \(1.8441\) | |
| 5880.z6 | 5880bc6 | \([0, 1, 0, 258704, 40539680]\) | \(7947184069438/7533176175\) | \(-1815082278528153600\) | \([2]\) | \(98304\) | \(2.1907\) |
Rank
sage: E.rank()
The elliptic curves in class 5880.z have rank \(0\).
Complex multiplication
The elliptic curves in class 5880.z do not have complex multiplication.Modular form 5880.2.a.z
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.
