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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 304704en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304704.en2 | 304704en1 | \([0, 0, 0, -141769884, -651975800528]\) | \(-14647977776/59049\) | \(-1270312404523503006892032\) | \([2]\) | \(67829760\) | \(3.4817\) | \(\Gamma_0(N)\)-optimal |
| 304704.en1 | 304704en2 | \([0, 0, 0, -2270508204, -41642109395120]\) | \(15043017316604/243\) | \(20910492255530913693696\) | \([2]\) | \(135659520\) | \(3.8283\) |
Rank
sage: E.rank()
The elliptic curves in class 304704en have rank \(0\).
Complex multiplication
The elliptic curves in class 304704en do not have complex multiplication.Modular form 304704.2.a.en
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 Cremona 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 Cremona labels.
