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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 3822.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3822.w1 | 3822v2 | \([1, 1, 1, -180050305, 929830670369]\) | \(-5486773802537974663600129/2635437714\) | \(-310056611614386\) | \([]\) | \(395136\) | \(3.0195\) | |
3822.w2 | 3822v1 | \([1, 1, 1, 34985, 28472429]\) | \(40251338884511/2997011332224\) | \(-352595386224821376\) | \([]\) | \(56448\) | \(2.0465\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3822.w have rank \(0\).
Complex multiplication
The elliptic curves in class 3822.w do not have complex multiplication.Modular form 3822.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.