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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 53040l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53040.w2 | 53040l1 | \([0, -1, 0, 45, -1350]\) | \(615962624/48481875\) | \(-775710000\) | \([2]\) | \(24576\) | \(0.38529\) | \(\Gamma_0(N)\)-optimal |
| 53040.w1 | 53040l2 | \([0, -1, 0, -1580, -22800]\) | \(1705021456336/68471325\) | \(17528659200\) | \([2]\) | \(49152\) | \(0.73186\) |
Rank
sage: E.rank()
The elliptic curves in class 53040l have rank \(1\).
Complex multiplication
The elliptic curves in class 53040l do not have complex multiplication.Modular form 53040.2.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 Cremona 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 Cremona labels.
