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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 83942a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83942.c2 | 83942a1 | \([1, 0, 1, -34286, -2447144]\) | \(-413493625/152\) | \(-1638440730008\) | \([]\) | \(211968\) | \(1.3116\) | \(\Gamma_0(N)\)-optimal |
| 83942.c3 | 83942a2 | \([1, 0, 1, 20939, -9286208]\) | \(94196375/3511808\) | \(-37854534626104832\) | \([]\) | \(635904\) | \(1.8609\) | |
| 83942.c1 | 83942a3 | \([1, 0, 1, -188916, 254207730]\) | \(-69173457625/2550136832\) | \(-27488474030541897728\) | \([]\) | \(1907712\) | \(2.4102\) |
Rank
sage: E.rank()
The elliptic curves in class 83942a have rank \(0\).
Complex multiplication
The elliptic curves in class 83942a do not have complex multiplication.Modular form 83942.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
