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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 216384.gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
216384.gm1 | 216384w2 | \([0, 1, 0, -439553, -112313601]\) | \(104453838382375/14904\) | \(1340099002368\) | \([2]\) | \(884736\) | \(1.7367\) | |
216384.gm2 | 216384w1 | \([0, 1, 0, -27393, -1772289]\) | \(-25282750375/304704\) | \(-27397579603968\) | \([2]\) | \(442368\) | \(1.3901\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 216384.gm have rank \(0\).
Complex multiplication
The elliptic curves in class 216384.gm do not have complex multiplication.Modular form 216384.2.a.gm
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.