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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 12880.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12880.v1 | 12880l4 | \([0, -1, 0, -2669296, 1679469120]\) | \(513516182162686336369/1944885031250\) | \(7966249088000000\) | \([2]\) | \(359424\) | \(2.2658\) | |
12880.v2 | 12880l3 | \([0, -1, 0, -169296, 25469120]\) | \(131010595463836369/7704101562500\) | \(31556000000000000\) | \([2]\) | \(179712\) | \(1.9192\) | |
12880.v3 | 12880l2 | \([0, -1, 0, -45456, 414656]\) | \(2535986675931409/1450751712200\) | \(5942279013171200\) | \([2]\) | \(119808\) | \(1.7165\) | |
12880.v4 | 12880l1 | \([0, -1, 0, -29456, -1927744]\) | \(690080604747409/3406760000\) | \(13954088960000\) | \([2]\) | \(59904\) | \(1.3699\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12880.v have rank \(0\).
Complex multiplication
The elliptic curves in class 12880.v do not have complex multiplication.Modular form 12880.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.