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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 68445.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68445.q1 | 68445b2 | \([0, 0, 1, -27378, -1735081]\) | \(884736/5\) | \(12825821008845\) | \([]\) | \(155520\) | \(1.3571\) | |
| 68445.q2 | 68445b1 | \([0, 0, 1, -2028, 33504]\) | \(2359296/125\) | \(48871441125\) | \([]\) | \(51840\) | \(0.80784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68445.q have rank \(1\).
Complex multiplication
The elliptic curves in class 68445.q do not have complex multiplication.Modular form 68445.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
