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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2880.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.n1 | 2880a2 | \([0, 0, 0, -4428, 112752]\) | \(3721734/25\) | \(64497254400\) | \([2]\) | \(3072\) | \(0.90887\) | |
| 2880.n2 | 2880a1 | \([0, 0, 0, -108, 3888]\) | \(-108/5\) | \(-6449725440\) | \([2]\) | \(1536\) | \(0.56230\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2880.n have rank \(1\).
Complex multiplication
The elliptic curves in class 2880.n do not have complex multiplication.Modular form 2880.2.a.n
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.
