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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 270480.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.l1 | 270480l2 | \([0, -1, 0, -190136, -31833360]\) | \(1577505447721/838350\) | \(403992736358400\) | \([2]\) | \(1990656\) | \(1.7525\) | |
| 270480.l2 | 270480l1 | \([0, -1, 0, -9816, -674064]\) | \(-217081801/285660\) | \(-137656784240640\) | \([2]\) | \(995328\) | \(1.4059\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270480.l have rank \(2\).
Complex multiplication
The elliptic curves in class 270480.l do not have complex multiplication.Modular form 270480.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
