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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 30576co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30576.da3 | 30576co1 | \([0, 1, 0, -44312, -3506028]\) | \(19968681097/628992\) | \(303105146093568\) | \([2]\) | \(110592\) | \(1.5536\) | \(\Gamma_0(N)\)-optimal |
| 30576.da2 | 30576co2 | \([0, 1, 0, -107032, 8561300]\) | \(281397674377/96589584\) | \(46545583996993536\) | \([2, 2]\) | \(221184\) | \(1.9002\) | |
| 30576.da4 | 30576co3 | \([0, 1, 0, 316328, 59872532]\) | \(7264187703863/7406095788\) | \(-3568925750732439552\) | \([2]\) | \(442368\) | \(2.2467\) | |
| 30576.da1 | 30576co4 | \([0, 1, 0, -1533912, 730562580]\) | \(828279937799497/193444524\) | \(93219040477495296\) | \([2]\) | \(442368\) | \(2.2467\) |
Rank
sage: E.rank()
The elliptic curves in class 30576co have rank \(0\).
Complex multiplication
The elliptic curves in class 30576co do not have complex multiplication.Modular form 30576.2.a.co
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
