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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 102245.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102245.d1 | 102245l1 | \([1, 0, 0, -20875, -248808]\) | \(117649/65\) | \(555814127625185\) | \([2]\) | \(470400\) | \(1.5198\) | \(\Gamma_0(N)\)-optimal |
102245.d2 | 102245l2 | \([1, 0, 0, 81370, -1946075]\) | \(6967871/4225\) | \(-36127918295637025\) | \([2]\) | \(940800\) | \(1.8664\) |
Rank
sage: E.rank()
The elliptic curves in class 102245.d have rank \(1\).
Complex multiplication
The elliptic curves in class 102245.d do not have complex multiplication.Modular form 102245.2.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.