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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 304200d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.d2 | 304200d1 | \([0, 0, 0, -738075, 533659750]\) | \(-1735192372/3796875\) | \(-97297989750000000000\) | \([2]\) | \(11059200\) | \(2.5241\) | \(\Gamma_0(N)\)-optimal |
304200.d1 | 304200d2 | \([0, 0, 0, -15363075, 23158534750]\) | \(7824392006186/7381125\) | \(378294584148000000000\) | \([2]\) | \(22118400\) | \(2.8707\) |
Rank
sage: E.rank()
The elliptic curves in class 304200d have rank \(1\).
Complex multiplication
The elliptic curves in class 304200d do not have complex multiplication.Modular form 304200.2.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.