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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 360640.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360640.cr1 | 360640cr1 | \([0, -1, 0, -516030825, 4512093991777]\) | \(-126142795384287538429696/9315359375\) | \(-1122245340272000000\) | \([]\) | \(54411264\) | \(3.3598\) | \(\Gamma_0(N)\)-optimal |
| 360640.cr2 | 360640cr2 | \([0, -1, 0, -510836825, 4607365220977]\) | \(-122372013839654770813696/5297595236711512175\) | \(-638214944771965640577612800\) | \([]\) | \(163233792\) | \(3.9091\) |
Rank
sage: E.rank()
The elliptic curves in class 360640.cr have rank \(1\).
Complex multiplication
The elliptic curves in class 360640.cr do not have complex multiplication.Modular form 360640.2.a.cr
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.
