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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 374850.dx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.dx1 | 374850dx2 | \([1, -1, 0, -594792, 107512866]\) | \(5956317014383/2172381210\) | \(8487459444013593750\) | \([2]\) | \(7077888\) | \(2.3325\) | |
374850.dx2 | 374850dx1 | \([1, -1, 0, 113958, 11831616]\) | \(41890384817/39795300\) | \(-155479615298437500\) | \([2]\) | \(3538944\) | \(1.9859\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374850.dx have rank \(2\).
Complex multiplication
The elliptic curves in class 374850.dx do not have complex multiplication.Modular form 374850.2.a.dx
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 LMFDB 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 LMFDB labels.