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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 144400.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144400.d1 | 144400b2 | \([0, 1, 0, -42068533, 78188230563]\) | \(7575076864/1953125\) | \(2122945380125000000000000\) | \([]\) | \(24820992\) | \(3.3772\) | |
144400.d2 | 144400b1 | \([0, 1, 0, -14632533, -21541629437]\) | \(318767104/125\) | \(135868504328000000000\) | \([]\) | \(8273664\) | \(2.8279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144400.d have rank \(0\).
Complex multiplication
The elliptic curves in class 144400.d do not have complex multiplication.Modular form 144400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.