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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 388710v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388710.v2 | 388710v1 | \([1, -1, 0, -1240485, -539476075]\) | \(-289581579184798874961/5081260310000000\) | \(-3704238765990000000\) | \([]\) | \(12216288\) | \(2.3604\) | \(\Gamma_0(N)\)-optimal |
388710.v1 | 388710v2 | \([1, -1, 0, -11437035, 65138641955]\) | \(-226953328047600468451761/2382836194386693393110\) | \(-1737087585707899483577190\) | \([]\) | \(85514016\) | \(3.3333\) |
Rank
sage: E.rank()
The elliptic curves in class 388710v have rank \(1\).
Complex multiplication
The elliptic curves in class 388710v do not have complex multiplication.Modular form 388710.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.