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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3360.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3360.n1 | 3360i2 | \([0, 1, 0, -65576, -6485076]\) | \(60910917333827912/3255076125\) | \(1666598976000\) | \([2]\) | \(9216\) | \(1.4126\) | |
| 3360.n2 | 3360i3 | \([0, 1, 0, -21201, 1100799]\) | \(257307998572864/19456203375\) | \(79692609024000\) | \([2]\) | \(9216\) | \(1.4126\) | |
| 3360.n3 | 3360i1 | \([0, 1, 0, -4326, -90576]\) | \(139927692143296/27348890625\) | \(1750329000000\) | \([2, 2]\) | \(4608\) | \(1.0660\) | \(\Gamma_0(N)\)-optimal |
| 3360.n4 | 3360i4 | \([0, 1, 0, 8904, -524520]\) | \(152461584507448/322998046875\) | \(-165375000000000\) | \([2]\) | \(9216\) | \(1.4126\) |
Rank
sage: E.rank()
The elliptic curves in class 3360.n have rank \(0\).
Complex multiplication
The elliptic curves in class 3360.n do not have complex multiplication.Modular form 3360.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
