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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 378560ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
378560.ev1 | 378560ev1 | \([0, 0, 0, -1856972, -48263696]\) | \(2238719766084/1292374265\) | \(408816434129822351360\) | \([2]\) | \(9289728\) | \(2.6445\) | \(\Gamma_0(N)\)-optimal |
378560.ev2 | 378560ev2 | \([0, 0, 0, 7417748, -385863504]\) | \(71346044015118/41389887175\) | \(-26185705707965589094400\) | \([2]\) | \(18579456\) | \(2.9911\) |
Rank
sage: E.rank()
The elliptic curves in class 378560ev have rank \(0\).
Complex multiplication
The elliptic curves in class 378560ev do not have complex multiplication.Modular form 378560.2.a.ev
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.