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SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 417600.fx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417600.fx1 | 417600fx2 | \([0, 0, 0, -93758700, 350456398000]\) | \(-30526075007211889/103499257854\) | \(-309047127963918336000000\) | \([]\) | \(42147840\) | \(3.3714\) | \(\Gamma_0(N)\)-optimal* |
417600.fx2 | 417600fx1 | \([0, 0, 0, -14700, -236882000]\) | \(-117649/8118144\) | \(-24240648093696000000\) | \([]\) | \(6021120\) | \(2.3984\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 417600.fx have rank \(1\).
Complex multiplication
The elliptic curves in class 417600.fx do not have complex multiplication.Modular form 417600.2.a.fx
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.