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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 402930z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
402930.z1 | 402930z1 | \([1, -1, 0, -928395, 344190325]\) | \(68523370149961/80586000\) | \(104074237749834000\) | \([2]\) | \(9584640\) | \(2.1771\) | \(\Gamma_0(N)\)-optimal |
402930.z2 | 402930z2 | \([1, -1, 0, -688815, 525839881]\) | \(-27986475935881/76236187500\) | \(-98456594234928187500\) | \([2]\) | \(19169280\) | \(2.5237\) |
Rank
sage: E.rank()
The elliptic curves in class 402930z have rank \(1\).
Complex multiplication
The elliptic curves in class 402930z do not have complex multiplication.Modular form 402930.2.a.z
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.