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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 30006d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30006.e1 | 30006d1 | \([1, -1, 1, -914, 10833]\) | \(115714886617/320064\) | \(233326656\) | \([2]\) | \(12288\) | \(0.47850\) | \(\Gamma_0(N)\)-optimal |
30006.e2 | 30006d2 | \([1, -1, 1, -554, 19185]\) | \(-25750777177/200080008\) | \(-145858325832\) | \([2]\) | \(24576\) | \(0.82507\) |
Rank
sage: E.rank()
The elliptic curves in class 30006d have rank \(1\).
Complex multiplication
The elliptic curves in class 30006d do not have complex multiplication.Modular form 30006.2.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 Cremona 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 Cremona labels.