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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6480.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6480.k1 | 6480l2 | \([0, 0, 0, -3603, 83602]\) | \(-15590912409/78125\) | \(-25920000000\) | \([]\) | \(5376\) | \(0.84551\) | |
| 6480.k2 | 6480l1 | \([0, 0, 0, -3, -62]\) | \(-9/5\) | \(-1658880\) | \([]\) | \(768\) | \(-0.12744\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6480.k have rank \(0\).
Complex multiplication
The elliptic curves in class 6480.k do not have complex multiplication.Modular form 6480.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
