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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 183872d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
183872.e1 | 183872d1 | \([0, 1, 0, -2929, -25713]\) | \(35152/17\) | \(1344401457152\) | \([2]\) | \(294912\) | \(1.0208\) | \(\Gamma_0(N)\)-optimal |
183872.e2 | 183872d2 | \([0, 1, 0, 10591, -185249]\) | \(415292/289\) | \(-91419299086336\) | \([2]\) | \(589824\) | \(1.3674\) |
Rank
sage: E.rank()
The elliptic curves in class 183872d have rank \(1\).
Complex multiplication
The elliptic curves in class 183872d do not have complex multiplication.Modular form 183872.2.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.