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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7350c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.s2 | 7350c1 | \([1, 1, 0, -87000, -9841320]\) | \(505318200625/4251528\) | \(612730321648200\) | \([]\) | \(60480\) | \(1.6629\) | \(\Gamma_0(N)\)-optimal |
7350.s1 | 7350c2 | \([1, 1, 0, -7032750, -7181467110]\) | \(266916252066900625/162\) | \(23347444050\) | \([]\) | \(181440\) | \(2.2122\) |
Rank
sage: E.rank()
The elliptic curves in class 7350c have rank \(1\).
Complex multiplication
The elliptic curves in class 7350c do not have complex multiplication.Modular form 7350.2.a.c
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 Cremona 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 Cremona labels.