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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 120213h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120213.f3 | 120213h1 | \([0, 0, 1, -10830, 430402]\) | \(4096000/37\) | \(1268968548213\) | \([]\) | \(142560\) | \(1.1450\) | \(\Gamma_0(N)\)-optimal |
| 120213.f2 | 120213h2 | \([0, 0, 1, -75810, -7779821]\) | \(1404928000/50653\) | \(1737217942503597\) | \([]\) | \(427680\) | \(1.6943\) | |
| 120213.f1 | 120213h3 | \([0, 0, 1, -6086460, -5779566590]\) | \(727057727488000/37\) | \(1268968548213\) | \([]\) | \(1283040\) | \(2.2436\) |
Rank
sage: E.rank()
The elliptic curves in class 120213h have rank \(1\).
Complex multiplication
The elliptic curves in class 120213h do not have complex multiplication.Modular form 120213.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
