Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9075.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9075.d1 | 9075d1 | \([1, 1, 1, -338, -1594]\) | \(205379/75\) | \(1559765625\) | \([2]\) | \(4608\) | \(0.46435\) | \(\Gamma_0(N)\)-optimal |
9075.d2 | 9075d2 | \([1, 1, 1, 1037, -9844]\) | \(5929741/5625\) | \(-116982421875\) | \([2]\) | \(9216\) | \(0.81092\) |
Rank
sage: E.rank()
The elliptic curves in class 9075.d have rank \(1\).
Complex multiplication
The elliptic curves in class 9075.d do not have complex multiplication.Modular form 9075.2.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 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.