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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 300560.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 300560.d1 | 300560d2 | \([0, 1, 0, -818114896, -9006830969196]\) | \(3009261308803109129809313/85820312500000000\) | \(1727017760000000000000000\) | \([2]\) | \(70778880\) | \(3.7520\) | |
| 300560.d2 | 300560d1 | \([0, 1, 0, -53207376, -128702366060]\) | \(827813553991775477153/123566310400000000\) | \(2486604935148339200000000\) | \([2]\) | \(35389440\) | \(3.4055\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 300560.d have rank \(0\).
Complex multiplication
The elliptic curves in class 300560.d do not have complex multiplication.Modular form 300560.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
