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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 101430.df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.df1 | 101430ee2 | \([1, -1, 1, -6884093, -6949609019]\) | \(420676324562824569/56350000000\) | \(4832920918350000000\) | \([2]\) | \(4128768\) | \(2.6042\) | |
| 101430.df2 | 101430ee1 | \([1, -1, 1, -392573, -128319803]\) | \(-78013216986489/37918720000\) | \(-3252141527685120000\) | \([2]\) | \(2064384\) | \(2.2576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101430.df have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.df do not have complex multiplication.Modular form 101430.2.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.
