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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 414810.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414810.f1 | 414810f2 | \([1, -1, 0, -843316485, 9426330954755]\) | \(90984613355465878035683930961/249396782289047639290\) | \(181810254288715729042410\) | \([]\) | \(139142752\) | \(3.6964\) | \(\Gamma_0(N)\)-optimal* |
414810.f2 | 414810f1 | \([1, -1, 0, -8701935, -9871189075]\) | \(99964020929586731506161/81651246490000000\) | \(59523758691210000000\) | \([]\) | \(19877536\) | \(2.7234\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414810.f have rank \(1\).
Complex multiplication
The elliptic curves in class 414810.f do not have complex multiplication.Modular form 414810.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.