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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 385112.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 385112.m1 | 385112m3 | \([0, 0, 0, -8385179, 2766605462]\) | \(215062038362754/113550802729\) | \(34426048570677536933888\) | \([2]\) | \(18923520\) | \(3.0160\) | |
| 385112.m2 | 385112m2 | \([0, 0, 0, -4809139, -4027155330]\) | \(81144432781668/740329681\) | \(112225651179439522816\) | \([2, 2]\) | \(9461760\) | \(2.6694\) | |
| 385112.m3 | 385112m1 | \([0, 0, 0, -4798559, -4045892510]\) | \(322440248841552/27209\) | \(1031144576973056\) | \([2]\) | \(4730880\) | \(2.3228\) | \(\Gamma_0(N)\)-optimal |
| 385112.m4 | 385112m4 | \([0, 0, 0, -1402379, -9621736602]\) | \(-1006057824354/131332646081\) | \(-39817103395477915666432\) | \([2]\) | \(18923520\) | \(3.0160\) |
Rank
sage: E.rank()
The elliptic curves in class 385112.m have rank \(0\).
Complex multiplication
The elliptic curves in class 385112.m do not have complex multiplication.Modular form 385112.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
