Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 304a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304.d2 | 304a1 | \([0, 1, 0, 0, -76]\) | \(-1/608\) | \(-2490368\) | \([]\) | \(48\) | \(-0.093787\) | \(\Gamma_0(N)\)-optimal |
304.d1 | 304a2 | \([0, 1, 0, -1120, 15604]\) | \(-37966934881/4952198\) | \(-20284203008\) | \([]\) | \(240\) | \(0.71093\) |
Rank
sage: E.rank()
The elliptic curves in class 304a have rank \(1\).
Complex multiplication
The elliptic curves in class 304a do not have complex multiplication.Modular form 304.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.