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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4410.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.d1 | 4410a2 | \([1, -1, 0, -87915, -10011275]\) | \(68971442301/400\) | \(435818955600\) | \([2]\) | \(14336\) | \(1.4236\) | |
4410.d2 | 4410a1 | \([1, -1, 0, -5595, -149339]\) | \(17779581/1280\) | \(1394620657920\) | \([2]\) | \(7168\) | \(1.0770\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4410.d have rank \(0\).
Complex multiplication
The elliptic curves in class 4410.d do not have complex multiplication.Modular form 4410.2.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.