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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 13200.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.d1 | 13200bl1 | \([0, -1, 0, -14448, -664128]\) | \(-3257444411545/2737152\) | \(-280284364800\) | \([]\) | \(28800\) | \(1.1243\) | \(\Gamma_0(N)\)-optimal |
| 13200.d2 | 13200bl2 | \([0, -1, 0, 99792, 5598912]\) | \(2747555975/1932612\) | \(-77304480000000000\) | \([]\) | \(144000\) | \(1.9290\) |
Rank
sage: E.rank()
The elliptic curves in class 13200.d have rank \(0\).
Complex multiplication
The elliptic curves in class 13200.d do not have complex multiplication.Modular form 13200.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
