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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3120.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3120.j1 | 3120s4 | \([0, -1, 0, -13961240, 20083149552]\) | \(73474353581350183614361/576510977802240\) | \(2361388965077975040\) | \([2]\) | \(103680\) | \(2.6985\) | |
| 3120.j2 | 3120s3 | \([0, -1, 0, -854040, 327977712]\) | \(-16818951115904497561/1592332281446400\) | \(-6522193024804454400\) | \([2]\) | \(51840\) | \(2.3520\) | |
| 3120.j3 | 3120s2 | \([0, -1, 0, -256040, -1791888]\) | \(453198971846635561/261896250564000\) | \(1072727042310144000\) | \([2]\) | \(34560\) | \(2.1492\) | |
| 3120.j4 | 3120s1 | \([0, -1, 0, 63960, -255888]\) | \(7064514799444439/4094064000000\) | \(-16769286144000000\) | \([2]\) | \(17280\) | \(1.8027\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3120.j have rank \(0\).
Complex multiplication
The elliptic curves in class 3120.j do not have complex multiplication.Modular form 3120.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
