Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 14994.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14994.a1 | 14994ba2 | \([1, -1, 0, -308709, 65963029]\) | \(37936442980801/88817792\) | \(7617557495624832\) | \([2]\) | \(258048\) | \(1.9277\) | |
14994.a2 | 14994ba1 | \([1, -1, 0, -26469, 201109]\) | \(23912763841/13647872\) | \(1170525041344512\) | \([2]\) | \(129024\) | \(1.5811\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14994.a have rank \(1\).
Complex multiplication
The elliptic curves in class 14994.a do not have complex multiplication.Modular form 14994.2.a.a
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.