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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 40293.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40293.h1 | 40293j3 | \([0, 0, 1, -2040060, -1121534208]\) | \(727057727488000/37\) | \(47784314853\) | \([]\) | \(243000\) | \(1.9703\) | |
| 40293.h2 | 40293j2 | \([0, 0, 1, -25410, -1509687]\) | \(1404928000/50653\) | \(65416727033757\) | \([]\) | \(81000\) | \(1.4210\) | |
| 40293.h3 | 40293j1 | \([0, 0, 1, -3630, 83520]\) | \(4096000/37\) | \(47784314853\) | \([]\) | \(27000\) | \(0.87172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40293.h have rank \(0\).
Complex multiplication
The elliptic curves in class 40293.h do not have complex multiplication.Modular form 40293.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
