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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 32064i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32064.s2 | 32064i1 | \([0, 1, 0, -3233, -88641]\) | \(-14260515625/4382748\) | \(-1148911091712\) | \([2]\) | \(36864\) | \(1.0278\) | \(\Gamma_0(N)\)-optimal |
32064.s1 | 32064i2 | \([0, 1, 0, -55073, -4992705]\) | \(70470585447625/4518018\) | \(1184371310592\) | \([2]\) | \(73728\) | \(1.3744\) |
Rank
sage: E.rank()
The elliptic curves in class 32064i have rank \(1\).
Complex multiplication
The elliptic curves in class 32064i do not have complex multiplication.Modular form 32064.2.a.i
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.