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SageMath
E = EllipticCurve("il1")
E.isogeny_class()
Elliptic curves in class 366912.il
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
366912.il1 | 366912il2 | \([0, 0, 0, -32340, 2217152]\) | \(10648000/117\) | \(41101869699072\) | \([2]\) | \(737280\) | \(1.4269\) | |
366912.il2 | 366912il1 | \([0, 0, 0, -3675, -30184]\) | \(1000000/507\) | \(2782939094208\) | \([2]\) | \(368640\) | \(1.0804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 366912.il have rank \(1\).
Complex multiplication
The elliptic curves in class 366912.il do not have complex multiplication.Modular form 366912.2.a.il
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.