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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 444675.es
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 444675.es1 | 444675es1 | \([0, 1, 1, -138343, 20730364]\) | \(-56197120/3267\) | \(-17022897893769075\) | \([]\) | \(3265920\) | \(1.8707\) | \(\Gamma_0(N)\)-optimal |
| 444675.es2 | 444675es2 | \([0, 1, 1, 751007, 37005469]\) | \(8990228480/5314683\) | \(-27692472006963669675\) | \([]\) | \(9797760\) | \(2.4200\) |
Rank
sage: E.rank()
The elliptic curves in class 444675.es have rank \(0\).
Complex multiplication
The elliptic curves in class 444675.es do not have complex multiplication.Modular form 444675.2.a.es
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.
