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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 30153h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30153.g3 | 30153h1 | \([1, 0, 1, -805, 7523]\) | \(389017/57\) | \(8438045673\) | \([2]\) | \(18480\) | \(0.62959\) | \(\Gamma_0(N)\)-optimal |
| 30153.g2 | 30153h2 | \([1, 0, 1, -3450, -70769]\) | \(30664297/3249\) | \(480968603361\) | \([2, 2]\) | \(36960\) | \(0.97616\) | |
| 30153.g4 | 30153h3 | \([1, 0, 1, 4485, -346907]\) | \(67419143/390963\) | \(-57876555271107\) | \([2]\) | \(73920\) | \(1.3227\) | |
| 30153.g1 | 30153h4 | \([1, 0, 1, -53705, -4794739]\) | \(115714886617/1539\) | \(227827233171\) | \([2]\) | \(73920\) | \(1.3227\) |
Rank
sage: E.rank()
The elliptic curves in class 30153h have rank \(0\).
Complex multiplication
The elliptic curves in class 30153h do not have complex multiplication.Modular form 30153.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
