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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 355740.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.du1 | 355740du2 | \([0, 1, 0, -3061340, 2056996500]\) | \(59466754384/121275\) | \(6470764581195129600\) | \([2]\) | \(11059200\) | \(2.4960\) | |
| 355740.du2 | 355740du1 | \([0, 1, 0, -126485, 54251448]\) | \(-67108864/343035\) | \(-1143938738461281840\) | \([2]\) | \(5529600\) | \(2.1494\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 355740.du have rank \(0\).
Complex multiplication
The elliptic curves in class 355740.du do not have complex multiplication.Modular form 355740.2.a.du
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.
