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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1520.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1520.d1 | 1520j2 | \([0, -1, 0, -44480, 3625600]\) | \(-2376117230685121/342950\) | \(-1404723200\) | \([]\) | \(1728\) | \(1.1643\) | |
| 1520.d2 | 1520j1 | \([0, -1, 0, -480, 6400]\) | \(-2992209121/2375000\) | \(-9728000000\) | \([]\) | \(576\) | \(0.61498\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1520.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1520.d do not have complex multiplication.Modular form 1520.2.a.d
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.
