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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 14400t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.e2 | 14400t1 | \([0, 0, 0, -60, 400]\) | \(-432\) | \(-55296000\) | \([2]\) | \(4096\) | \(0.17407\) | \(\Gamma_0(N)\)-optimal |
14400.e1 | 14400t2 | \([0, 0, 0, -1260, 17200]\) | \(1000188\) | \(221184000\) | \([2]\) | \(8192\) | \(0.52064\) |
Rank
sage: E.rank()
The elliptic curves in class 14400t have rank \(2\).
Complex multiplication
The elliptic curves in class 14400t do not have complex multiplication.Modular form 14400.2.a.t
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.