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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 13680c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13680.d2 | 13680c1 | \([0, 0, 0, -483, 4082]\) | \(450714348/475\) | \(13132800\) | \([2]\) | \(5120\) | \(0.28284\) | \(\Gamma_0(N)\)-optimal |
13680.d1 | 13680c2 | \([0, 0, 0, -603, 1898]\) | \(438512454/225625\) | \(12476160000\) | \([2]\) | \(10240\) | \(0.62941\) |
Rank
sage: E.rank()
The elliptic curves in class 13680c have rank \(2\).
Complex multiplication
The elliptic curves in class 13680c do not have complex multiplication.Modular form 13680.2.a.c
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.