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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 111540l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111540.r2 | 111540l1 | \([0, -1, 0, -225, 21150]\) | \(-16384/2475\) | \(-191141636400\) | \([2]\) | \(103680\) | \(0.84407\) | \(\Gamma_0(N)\)-optimal |
111540.r1 | 111540l2 | \([0, -1, 0, -12900, 563640]\) | \(192143824/1815\) | \(2242728533760\) | \([2]\) | \(207360\) | \(1.1906\) |
Rank
sage: E.rank()
The elliptic curves in class 111540l have rank \(1\).
Complex multiplication
The elliptic curves in class 111540l do not have complex multiplication.Modular form 111540.2.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.