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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 377520.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.fk1 | 377520fk2 | \([0, 1, 0, -89096, -9199500]\) | \(10779215329/1232010\) | \(8939851233730560\) | \([2]\) | \(2949120\) | \(1.7931\) | |
| 377520.fk2 | 377520fk1 | \([0, 1, 0, 7704, -719820]\) | \(6967871/35100\) | \(-254696616345600\) | \([2]\) | \(1474560\) | \(1.4465\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.fk have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.fk do not have complex multiplication.Modular form 377520.2.a.fk
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.
