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SageMath
E = EllipticCurve("iu1")
E.isogeny_class()
Elliptic curves in class 118800.iu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 118800.iu1 | 118800fq2 | \([0, 0, 0, -16725, -832525]\) | \(212919686400/11\) | \(26730000\) | \([]\) | \(124416\) | \(0.89758\) | |
| 118800.iu2 | 118800fq1 | \([0, 0, 0, -225, -925]\) | \(4665600/1331\) | \(359370000\) | \([]\) | \(41472\) | \(0.34827\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 118800.iu have rank \(0\).
Complex multiplication
The elliptic curves in class 118800.iu do not have complex multiplication.Modular form 118800.2.a.iu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
