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SageMath
E = EllipticCurve("ik1")
E.isogeny_class()
Elliptic curves in class 366912ik
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.ik2 | 366912ik1 | \([0, 0, 0, -3675, 30184]\) | \(1000000/507\) | \(2782939094208\) | \([2]\) | \(368640\) | \(1.0804\) | \(\Gamma_0(N)\)-optimal |
| 366912.ik1 | 366912ik2 | \([0, 0, 0, -32340, -2217152]\) | \(10648000/117\) | \(41101869699072\) | \([2]\) | \(737280\) | \(1.4269\) |
Rank
sage: E.rank()
The elliptic curves in class 366912ik have rank \(1\).
Complex multiplication
The elliptic curves in class 366912ik do not have complex multiplication.Modular form 366912.2.a.ik
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 Cremona 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 Cremona labels.
