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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 25872.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25872.u1 | 25872i2 | \([0, -1, 0, -21968, -1236192]\) | \(4866277250/43659\) | \(10519424391168\) | \([2]\) | \(73728\) | \(1.3215\) | |
25872.u2 | 25872i1 | \([0, -1, 0, -408, -46080]\) | \(-62500/7623\) | \(-918362446848\) | \([2]\) | \(36864\) | \(0.97495\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25872.u have rank \(1\).
Complex multiplication
The elliptic curves in class 25872.u do not have complex multiplication.Modular form 25872.2.a.u
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.