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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 194579.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194579.d1 | 194579d2 | \([1, 1, 1, -911352, 308744246]\) | \(15124197817/1294139\) | \(7162931055995759891\) | \([2]\) | \(4147200\) | \(2.3592\) | |
194579.d2 | 194579d1 | \([1, 1, 1, 61543, 22323958]\) | \(4657463/41503\) | \(-229714990133974807\) | \([2]\) | \(2073600\) | \(2.0126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 194579.d have rank \(0\).
Complex multiplication
The elliptic curves in class 194579.d do not have complex multiplication.Modular form 194579.2.a.d
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.