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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 54080dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54080.q2 | 54080dg1 | \([0, 1, 0, -351745, -79937025]\) | \(3803721481/26000\) | \(32898294480896000\) | \([2]\) | \(774144\) | \(2.0033\) | \(\Gamma_0(N)\)-optimal |
| 54080.q3 | 54080dg2 | \([0, 1, 0, -135425, -176978177]\) | \(-217081801/10562500\) | \(-13364932132864000000\) | \([2]\) | \(1548288\) | \(2.3499\) | |
| 54080.q1 | 54080dg3 | \([0, 1, 0, -2244545, 1241615935]\) | \(988345570681/44994560\) | \(56932472496859381760\) | \([2]\) | \(2322432\) | \(2.5526\) | |
| 54080.q4 | 54080dg4 | \([0, 1, 0, 1216575, 4728348223]\) | \(157376536199/7722894400\) | \(-9771925162156254822400\) | \([2]\) | \(4644864\) | \(2.8992\) |
Rank
sage: E.rank()
The elliptic curves in class 54080dg have rank \(1\).
Complex multiplication
The elliptic curves in class 54080dg do not have complex multiplication.Modular form 54080.2.a.dg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
