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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 369600d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.d2 | 369600d1 | \([0, -1, 0, -59333, 5954037]\) | \(-11550212096/922383\) | \(-1844766000000000\) | \([2]\) | \(2826240\) | \(1.6759\) | \(\Gamma_0(N)\)-optimal |
369600.d1 | 369600d2 | \([0, -1, 0, -966833, 366231537]\) | \(3123406998416/17787\) | \(569184000000000\) | \([2]\) | \(5652480\) | \(2.0225\) |
Rank
sage: E.rank()
The elliptic curves in class 369600d have rank \(1\).
Complex multiplication
The elliptic curves in class 369600d do not have complex multiplication.Modular form 369600.2.a.d
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.