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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 18032d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18032.u2 | 18032d1 | \([0, -1, 0, -1388, 26048]\) | \(-9826000/3703\) | \(-111527487232\) | \([2]\) | \(15360\) | \(0.82963\) | \(\Gamma_0(N)\)-optimal |
18032.u1 | 18032d2 | \([0, -1, 0, -23928, 1432544]\) | \(12576878500/1127\) | \(135772593152\) | \([2]\) | \(30720\) | \(1.1762\) |
Rank
sage: E.rank()
The elliptic curves in class 18032d have rank \(0\).
Complex multiplication
The elliptic curves in class 18032d do not have complex multiplication.Modular form 18032.2.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.