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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 63580.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63580.h1 | 63580i2 | \([0, -1, 0, -15005, -702503]\) | \(-5050365927424/171875\) | \(-12716000000\) | \([]\) | \(93312\) | \(1.0306\) | |
| 63580.h2 | 63580i1 | \([0, -1, 0, -45, -2375]\) | \(-139264/33275\) | \(-2461817600\) | \([]\) | \(31104\) | \(0.48126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63580.h have rank \(1\).
Complex multiplication
The elliptic curves in class 63580.h do not have complex multiplication.Modular form 63580.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
