Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 704.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 704.f1 | 704d2 | \([0, -1, 0, -309, -2003]\) | \(-199794688/1331\) | \(-21807104\) | \([]\) | \(192\) | \(0.24359\) | |
| 704.f2 | 704d1 | \([0, -1, 0, 11, -19]\) | \(8192/11\) | \(-180224\) | \([]\) | \(64\) | \(-0.30572\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 704.f have rank \(0\).
Complex multiplication
The elliptic curves in class 704.f do not have complex multiplication.Modular form 704.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
