Show commands:
SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 350658.df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.df1 | 350658df2 | \([1, -1, 1, -67592075, 213907537253]\) | \(26444015547214434625/46191222\) | \(59654483661968118\) | \([2]\) | \(20643840\) | \(2.9068\) | |
| 350658.df2 | 350658df1 | \([1, -1, 1, -4223165, 3345323105]\) | \(-6449916994998625/8532911772\) | \(-11019982235841031068\) | \([2]\) | \(10321920\) | \(2.5603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.df have rank \(1\).
Complex multiplication
The elliptic curves in class 350658.df do not have complex multiplication.Modular form 350658.2.a.df
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.
