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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 69300h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69300.s1 | 69300h1 | \([0, 0, 0, -1200, 14625]\) | \(28311552/2695\) | \(18191250000\) | \([2]\) | \(64512\) | \(0.70655\) | \(\Gamma_0(N)\)-optimal |
| 69300.s2 | 69300h2 | \([0, 0, 0, 1425, 69750]\) | \(2963088/21175\) | \(-2286900000000\) | \([2]\) | \(129024\) | \(1.0531\) |
Rank
sage: E.rank()
The elliptic curves in class 69300h have rank \(1\).
Complex multiplication
The elliptic curves in class 69300h do not have complex multiplication.Modular form 69300.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
