Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 425880d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.d2 | 425880d1 | \([0, 0, 0, -24208743, -45837606022]\) | \(792834915472/178605\) | \(353468955920688840960\) | \([2]\) | \(32587776\) | \(2.9353\) | \(\Gamma_0(N)\)-optimal* |
425880.d1 | 425880d2 | \([0, 0, 0, -26976963, -34703271538]\) | \(274274369428/93002175\) | \(736225339617663328742400\) | \([2]\) | \(65175552\) | \(3.2819\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 425880d have rank \(1\).
Complex multiplication
The elliptic curves in class 425880d do not have complex multiplication.Modular form 425880.2.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.