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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 63480h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63480.r4 | 63480h1 | \([0, 1, 0, 1940, 15968]\) | \(21296/15\) | \(-568457813760\) | \([2]\) | \(90112\) | \(0.94400\) | \(\Gamma_0(N)\)-optimal |
| 63480.r3 | 63480h2 | \([0, 1, 0, -8640, 126000]\) | \(470596/225\) | \(34107468825600\) | \([2, 2]\) | \(180224\) | \(1.2906\) | |
| 63480.r2 | 63480h3 | \([0, 1, 0, -72120, -7390032]\) | \(136835858/1875\) | \(568457813760000\) | \([2]\) | \(360448\) | \(1.6371\) | |
| 63480.r1 | 63480h4 | \([0, 1, 0, -114440, 14853360]\) | \(546718898/405\) | \(122786887772160\) | \([2]\) | \(360448\) | \(1.6371\) |
Rank
sage: E.rank()
The elliptic curves in class 63480h have rank \(0\).
Complex multiplication
The elliptic curves in class 63480h do not have complex multiplication.Modular form 63480.2.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.
