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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 102966.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102966.e1 | 102966d1 | \([1, 1, 0, -1218788, 514822800]\) | \(39616946929/226368\) | \(1144044210644601408\) | \([2]\) | \(4942080\) | \(2.3066\) | \(\Gamma_0(N)\)-optimal |
102966.e2 | 102966d2 | \([1, 1, 0, -532348, 1092118840]\) | \(-3301293169/100082952\) | \(-505810546631244397512\) | \([2]\) | \(9884160\) | \(2.6531\) |
Rank
sage: E.rank()
The elliptic curves in class 102966.e have rank \(0\).
Complex multiplication
The elliptic curves in class 102966.e do not have complex multiplication.Modular form 102966.2.a.e
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.