Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 324870l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
324870.l1 | 324870l1 | \([1, 1, 0, -683, 3837]\) | \(102963870703/38188800\) | \(13098758400\) | \([2]\) | \(258048\) | \(0.64129\) | \(\Gamma_0(N)\)-optimal |
324870.l2 | 324870l2 | \([1, 1, 0, 2117, 30157]\) | \(3056832103697/2848407120\) | \(-977003642160\) | \([2]\) | \(516096\) | \(0.98787\) |
Rank
sage: E.rank()
The elliptic curves in class 324870l have rank \(1\).
Complex multiplication
The elliptic curves in class 324870l do not have complex multiplication.Modular form 324870.2.a.l
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.