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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 6080.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6080.m1 | 6080g2 | \([0, 0, 0, -412, -3216]\) | \(472058064/475\) | \(7782400\) | \([2]\) | \(1536\) | \(0.24141\) | |
6080.m2 | 6080g1 | \([0, 0, 0, -32, -24]\) | \(3538944/1805\) | \(1848320\) | \([2]\) | \(768\) | \(-0.10516\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6080.m have rank \(0\).
Complex multiplication
The elliptic curves in class 6080.m do not have complex multiplication.Modular form 6080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.