Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 279174h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 279174.h4 | 279174h1 | \([1, 1, 0, 1342255, 4215948693]\) | \(11079872671250375/324440155855872\) | \(-7831196648341864455168\) | \([2]\) | \(22118400\) | \(2.8811\) | \(\Gamma_0(N)\)-optimal |
| 279174.h2 | 279174h2 | \([1, 1, 0, -32366705, 67514633781]\) | \(155355156733986861625/8291568305839392\) | \(200138302100411427318048\) | \([2]\) | \(44236800\) | \(3.2277\) | |
| 279174.h3 | 279174h3 | \([1, 1, 0, -12117920, -115820276736]\) | \(-8152944444844179625/235342826399858688\) | \(-5680603710881610671849472\) | \([2]\) | \(66355200\) | \(3.4304\) | |
| 279174.h1 | 279174h4 | \([1, 1, 0, -438265760, -3514519759872]\) | \(385693937170561837203625/2159357734550274048\) | \(52121646313390923802509312\) | \([2]\) | \(132710400\) | \(3.7770\) |
Rank
sage: E.rank()
The elliptic curves in class 279174h have rank \(1\).
Complex multiplication
The elliptic curves in class 279174h do not have complex multiplication.Modular form 279174.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
