Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 15456f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15456.u2 | 15456f1 | \([0, 1, 0, -7082, -349248]\) | \(-613864936718272/456986789343\) | \(-29247154517952\) | \([2]\) | \(39168\) | \(1.2832\) | \(\Gamma_0(N)\)-optimal |
| 15456.u1 | 15456f2 | \([0, 1, 0, -128752, -17821060]\) | \(461019267341732744/115946266023\) | \(59364488203776\) | \([2]\) | \(78336\) | \(1.6298\) |
Rank
sage: E.rank()
The elliptic curves in class 15456f have rank \(0\).
Complex multiplication
The elliptic curves in class 15456f do not have complex multiplication.Modular form 15456.2.a.f
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.
