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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 230384t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230384.t2 | 230384t1 | \([0, 1, 0, 60944, -1103148]\) | \(3449795831/2071552\) | \(-15031831481024512\) | \([2]\) | \(2457600\) | \(1.7934\) | \(\Gamma_0(N)\)-optimal |
230384.t1 | 230384t2 | \([0, 1, 0, -248816, -9156908]\) | \(234770924809/130960928\) | \(950293596441018368\) | \([2]\) | \(4915200\) | \(2.1399\) |
Rank
sage: E.rank()
The elliptic curves in class 230384t have rank \(1\).
Complex multiplication
The elliptic curves in class 230384t do not have complex multiplication.Modular form 230384.2.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.