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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 101430.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.dt1 | 101430eh1 | \([1, -1, 1, -10373, 226797]\) | \(1439069689/579600\) | \(49710043731600\) | \([2]\) | \(294912\) | \(1.3261\) | \(\Gamma_0(N)\)-optimal |
101430.dt2 | 101430eh2 | \([1, -1, 1, 33727, 1620357]\) | \(49471280711/41992020\) | \(-3601492668354420\) | \([2]\) | \(589824\) | \(1.6726\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.dt do not have complex multiplication.Modular form 101430.2.a.dt
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.