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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 217800.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
217800.di1 | 217800fu2 | \([0, 0, 0, -48675, -4023250]\) | \(821516/25\) | \(388119600000000\) | \([2]\) | \(663552\) | \(1.5754\) | |
217800.di2 | 217800fu1 | \([0, 0, 0, 825, -211750]\) | \(16/5\) | \(-19405980000000\) | \([2]\) | \(331776\) | \(1.2289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 217800.di have rank \(2\).
Complex multiplication
The elliptic curves in class 217800.di do not have complex multiplication.Modular form 217800.2.a.di
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.