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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 418950.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.f1 | 418950f2 | \([1, -1, 0, -663567, -205884659]\) | \(651038076963/7220000\) | \(358351500937500000\) | \([2]\) | \(8847360\) | \(2.1827\) | |
418950.f2 | 418950f1 | \([1, -1, 0, -75567, 2855341]\) | \(961504803/486400\) | \(24141574800000000\) | \([2]\) | \(4423680\) | \(1.8361\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950.f have rank \(1\).
Complex multiplication
The elliptic curves in class 418950.f do not have complex multiplication.Modular form 418950.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.