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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 224400be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.ex1 | 224400be1 | \([0, 1, 0, -361608, -83155212]\) | \(81706955619457/744505344\) | \(47648342016000000\) | \([2]\) | \(3440640\) | \(2.0224\) | \(\Gamma_0(N)\)-optimal |
| 224400.ex2 | 224400be2 | \([0, 1, 0, -105608, -198355212]\) | \(-2035346265217/264305213568\) | \(-16915533668352000000\) | \([2]\) | \(6881280\) | \(2.3690\) |
Rank
sage: E.rank()
The elliptic curves in class 224400be have rank \(1\).
Complex multiplication
The elliptic curves in class 224400be do not have complex multiplication.Modular form 224400.2.a.be
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.
