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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 3344e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3344.d1 | 3344e1 | \([0, -1, 0, -437, -3971]\) | \(-2258403328/480491\) | \(-1968091136\) | \([]\) | \(1728\) | \(0.50473\) | \(\Gamma_0(N)\)-optimal |
3344.d2 | 3344e2 | \([0, -1, 0, 3083, 22781]\) | \(790939860992/517504691\) | \(-2119699214336\) | \([]\) | \(5184\) | \(1.0540\) |
Rank
sage: E.rank()
The elliptic curves in class 3344e have rank \(0\).
Complex multiplication
The elliptic curves in class 3344e do not have complex multiplication.Modular form 3344.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.