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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 133200.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
133200.di1 | 133200er2 | \([0, 0, 0, -255075, -49582750]\) | \(1062144635427/54760\) | \(94625280000000\) | \([2]\) | \(663552\) | \(1.7511\) | |
133200.di2 | 133200er1 | \([0, 0, 0, -15075, -862750]\) | \(-219256227/59200\) | \(-102297600000000\) | \([2]\) | \(331776\) | \(1.4045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133200.di have rank \(0\).
Complex multiplication
The elliptic curves in class 133200.di do not have complex multiplication.Modular form 133200.2.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.