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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 2790.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.v1 | 2790x2 | \([1, -1, 1, -1966028, -1060550449]\) | \(1152829477932246539641/3188367360\) | \(2324319805440\) | \([2]\) | \(33280\) | \(2.0310\) | |
2790.v2 | 2790x1 | \([1, -1, 1, -122828, -16561969]\) | \(-281115640967896441/468084326400\) | \(-341233473945600\) | \([2]\) | \(16640\) | \(1.6845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2790.v have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.v do not have complex multiplication.Modular form 2790.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.