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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 24336.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24336.d1 | 24336bg2 | \([0, 0, 0, -456807, 118835730]\) | \(315978926832/169\) | \(5638330743552\) | \([2]\) | \(258048\) | \(1.7764\) | |
24336.d2 | 24336bg1 | \([0, 0, 0, -28392, 1878435]\) | \(-1213857792/28561\) | \(-59554868478768\) | \([2]\) | \(129024\) | \(1.4298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24336.d have rank \(0\).
Complex multiplication
The elliptic curves in class 24336.d do not have complex multiplication.Modular form 24336.2.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.