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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 215985.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215985.x1 | 215985n2 | \([1, 0, 0, -11942884951, -502352923627444]\) | \(79894575145988425306035539/833116937255859375\) | \(1964446158535445489501953125\) | \([2]\) | \(293787648\) | \(4.3941\) | |
215985.x2 | 215985n1 | \([1, 0, 0, -728151806, -8251967778405]\) | \(-18107368451406059457059/1996706851369453125\) | \(-4708130309790482184026484375\) | \([2]\) | \(146893824\) | \(4.0475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215985.x have rank \(0\).
Complex multiplication
The elliptic curves in class 215985.x do not have complex multiplication.Modular form 215985.2.a.x
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.